Chapter 23

A thin prism \(P_{1}\) with angle \(4^{\circ}\) and made from glass of refractive index \(1.54\) is combined with another thin prism \(P_{2}\) made from glass of refractive index \(1.72\) to produce dispersion without deviation. The angle of prism \(P_{2}\) is (a) \(3^{*}\) (b) \(4^{\circ}\) (c) \(5.33^{\circ}\) (d) \(2.6^{*}\)

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall \(3 \mathrm{~m}\) away by means of a large convex lens. What is the maximum possible foeal length of the lens required for the purpose? (a) \(0.88 \mathrm{~m}\) (b) \(0.90 \mathrm{~m}\) (c) \(0.75 \mathrm{~m}\) (d) \(0.63 \mathrm{~m}\)

The length of the compound microscope is \(14 \mathrm{~cm}\). The magnifying power for relaxed eye is \(25 .\) If the focal length of eyelens is \(5 \mathrm{~cm}\), then the object distance for objective lens will be (a) \(2.4 \mathrm{~cm}\) (b) \(2.1 \mathrm{~cm}\) (c) \(1.5 \mathrm{~cm}\) (d) \(1.8 \mathrm{~cm}\)

A convex lens of foeal length \(f\) produces a virtual image \(n\) times the size of the object. Then the distance of the object from the lens is (a) \((n-1) f\) (b) \((n+1) f\) (c) \(\left(\frac{n-1}{n}\right) f\) (d) \(\left(\frac{n+1}{n}\right) f\)

A concave lens of focal length \(20 \mathrm{~cm}\) produces an image half in size of the real object. The distance of the real object is (a) \(20 \mathrm{~cm}\) (b) \(30 \mathrm{~cm}\) (c) \(10 \mathrm{~cm}\) (d) \(60 \mathrm{~cm}\)

An object is kept at a distance of \(16 \mathrm{~cm}\) from a thin lens and the image formed is real. If the object is kept at a distance of \(6 \mathrm{~cm}\) from the same lens, the image formed is virtual. If the sizes of the image formed are equal the focal length of the lens will be (a) \(21 \mathrm{~cm}\) (b) \(11 \mathrm{~cm}\) (c) \(15 \mathrm{~cm}\) (d) \(17 \mathrm{~cm}\)

An object \(15 \mathrm{~cm}\) high is placed \(10 \mathrm{~cm}\) from the optical centre of a thin lens. Its image is formed \(25 \mathrm{~cm}\) from the optical centre in the same side of the lens as the object. The height of the image is [a) \(2.5 \mathrm{~cm}\) (b) \(0.2 \mathrm{~cm}\) (c) \(16.7 \mathrm{~cm}\) (d) \(37.5 \mathrm{~cm}\)

\(P\) is a point on the axis of a concave mirror. The image of \(P\) formed by the mirror, coincides with \(P . \mathrm{A}\) rectangular glass slab of thiekness \(t\) and refractive index \(\mu\) is now introduced between \(P\) and the mirror. For image of \(P\) to coincide with \(P\) again, the mirror must be moved (a) towards \(P\) by \((\bar{\mu}-\mathbf{I}) t\) (b) away from \(P\) by \((\mu-1) t\) (c) towards \(P\) by \(t\left(1-\frac{1}{\mu}\right)\) (d) away from \(P t\left(1-\frac{1}{\mu}\right)\)

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices \(\mu_{1}\) and \(\mu_{2}\) and \(R\) is the radius of curvature of the curved surface of the lenses, then focal length of the combination is (a) \(\frac{R}{2\left(\mu_{1}+\mu_{1}\right)}\) (b) \(\frac{R}{2\left(u_{1}-\mu_{1}\right)}\) (c) \(\frac{R}{\left(\mu_{1}-\mu_{2}\right)}\) (d) \(\frac{2 R}{\left(\mu_{1}+\mu_{2}\right)}\)

A convex lens of focal length \(\frac{1}{3} \mathrm{~m}\) forms a real, inverted image twice in size of he object. The distance of the object form the lens is (a) \(0.5 \mathrm{~m}\) (b) \(0.166 \mathrm{~m}\) (c) \(0.33 \mathrm{~m}\) (d) \(1 \mathrm{~m}\)

One of the refracting surfaces of a prism of angle \(30^{\circ}\) is silvered. A ray of light incident at an angle of \(60^{\circ}\) retraces its path. The refractive index of the material of prism is (a) \(\sqrt{3}\) (b) \(3 / 2\) (c) 2 (d) \(\sqrt{2}\)

The focal length of objective and eyepiece of a microscope are \(1 \mathrm{~cm}\) and \(5 \mathrm{em}\) respectively. If the magnifying power for relaxed eye is 45 , then of the tube is (a) \(9 \mathrm{~cm}\) (b) \(15 \mathrm{~cm}\) (c) \(12 \mathrm{~cm}\) (d) \(6 \mathrm{~cm}\)

A glass prism \(A B C\) (refractive index \(1.5\) ), immersed in water (refractive index \(4 / 3\) ). A ray of light is incident normally on face \(A B\). If it is totally reflected at face \(A C\), then (a) \(\sin \theta \geq \frac{8}{9}\) (b) \(\sin \theta \geq \frac{2}{3}\) (c) \(\sin \theta=\frac{\sqrt{3}}{2}\) (d) \(\frac{2}{3}<\sin \theta<\frac{8}{9}\)

A plane mirror as placed at the bottom of a tank containing a liquid of refractive index \(\mu . P\) is a small object at a height \(h\) above the mirror. An observer \(O\) vertically above \(P\) outside the liquid sees \(P\) and its image in a mirror. The apparent distance between these two will be (a) \(2 \mu h\) (b) \(\frac{2 h}{\mu}\) (c) \(\frac{2 h}{\mu-1}\) (d) \(H\left(1+\frac{1}{\mu}\right)\)

Light takes \(t_{1}\) second to travel a distance \(x\) in vacuum and the same light takes \(t_{2}\) second to travel \(10 x \mathrm{~cm}\) in a medium. Critical angle for corresponding medium will be (a) \(\sin ^{-1}\left(\frac{10 t_{2}}{t_{1}}\right)\) (b) \(\sin ^{-1}\left(\frac{t_{2}}{10 t_{1}}\right)\) (c) \(\sin ^{-1}\left(\frac{10 t_{1}}{t_{2}}\right)\) (d) \(\sin ^{-1}\left(\frac{t_{1}}{10 t_{2}}\right)\)

The power of a thin convex lens \(\left(_{a} n_{g}=1.5\right)\) is \(+5.0 \mathrm{D}\). When it is placed in a liquid of refractive index \(_{a} n_{e}\), then it behaves as a concave lens of focal length \(100 \mathrm{~cm}\). The refractive index of the liquid \(_{a} n_{l}\) will be (a) \(5 / 3\) (b) \(4 / 3\) (c) \(\sqrt{3}\) (d) \(5 / 4\)

A point object is placed at the centre of a glass sphere of radius, \(6 \mathrm{~cm}\) and refractive index, 1.5. The distance of the virtual image from the surface of the sphere is (a) \(2 \mathrm{~cm}\) (b) \(4 \mathrm{~cm}\) (c) \(6 \mathrm{~cm}\) (d) \(12 \mathrm{~cm}\)

A concave lens with unequal radii of curvature made of glass \(\left(\mu_{B}=15\right)\) has focal length of \(40 \mathrm{~cm}\). If it is immersed in a liquid of refractive index \(\mu=2\), then (a) it behaves like a convex lens of \(80 \mathrm{~cm}\) focal length (b) it behaves like a concave lens of \(20 \mathrm{~cm}\) focal length (c) its focal length becomes \(60 \mathrm{~cm}\) (d) nothing can be said

In order of obtain a real image of magnification 2 , using a converging lens of focal length \(20 \mathrm{~cm}\), where should an object be placed (a) \(50 \mathrm{~cm}\) (b) \(30 \mathrm{~cm}\) (c) \(-50 \mathrm{~cm}\) (d) \(-30 \mathrm{~cm}\)

A plano-convex lens of refractive index \(1.5\) and radius of curvature \(30 \mathrm{~cm}\) is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an objeet be placed in order to have a real image of the size of the object? (a) \(20 \mathrm{~cm}\) (b) \(30 \mathrm{~cm}\) (c) \(60 \mathrm{~cm}\) (d) \(80 \mathrm{~cm}\)

A virtual image twice as long as the object is formed by a convex lens when the object is \(10 \mathrm{~cm}\) away from it. A real image twice as long as the object will be formed when it is placed at a distance.....from the lens. (a) \(40 \mathrm{~cm}\) (b) \(30 \mathrm{~cm}\) (c) \(20 \mathrm{~cm}\) (d) \(15 \mathrm{~cm}\)

Double-convex lenses are to be manufactured from a glass of refractive index \(1.55\), with both faces of the same radius of curvature. What is the radius of curvature required, if the foeal length is to be \(20 \mathrm{~cm} ?\) [NCERT] (a) \(18 \mathrm{~m}\) (b) \(22 \mathrm{~cm}\) (c) \(17 \mathrm{~cm}\) (d) \(26 \mathrm{~cm}\)

The power of an achromatic convergent lens of two lenses is \(+2 \mathrm{D}\). The power of convex lens is \(+5 \mathrm{D}\). The ratio of dispersive power of convex and concave lens will be (a) \(5: 3\) (b) \(3: 5\) (c) \(2: 5\) (d) \(5: 2\)

The radius of the convex surface of plane-convex lens is \(20 \mathrm{~cm}\) and the refractive index of the material of the lens is 1.5. The focal length of the lens is (a) \(30 \mathrm{~cm}\) (b) \(50 \mathrm{~cm}\) (c) \(20 \mathrm{~cm}\) (d) \(40 \mathrm{~cm}\)

Monochromatic light of wavelength, \(\lambda_{1}\) travelling in medium of refractive index, \(n_{1}\) enters a denser medium of refractive index, \(n_{2}\) The wavelength in the second medium is (a) \(\lambda\left(\frac{n_{1}}{n_{2}}\right)\) (b) \(\lambda_{1}\left(\frac{n_{2}}{n_{1}}\right)\) (c) \(\lambda_{1}\) (d) \(\lambda\left(\frac{n_{1}-n_{1}}{n_{1}}\right)\)

What is the angle of incidence for an equilateral prism of refractive index \(\sqrt{3}\) so that the ray is parallel to the base inside the prism? (a) \(30^{\circ}\) (b) \(45^{\circ}\) (c) \(60^{*}\) (d) Either \(30^{\circ}\) or \(60^{\circ}\)

An astronomieal telescope has an angular magnification of magnitude 5 for distant object. The separation between the objective and the eyepiece is \(36 \mathrm{~cm}\) and the final image is formed at \(\infty\), The foeal length \(f_{0}\) of the objective and the focal length \(f_{e}\) of the eyepiece are (a) \(f_{0}=30 \mathrm{~cm}\) and \(f_{e}=6 \mathrm{~cm}\) (b) \(f_{0}=15 \mathrm{~cm}\) and \(f_{c}=12 \mathrm{~cm}\) (c) \(f_{0}=8.5 \mathrm{~cm}\) and \(f_{e}=12.9 \mathrm{~cm}\) (d) \(f_{0}=40 \mathrm{~cm}\) and \(f_{e}=11 \mathrm{~cm}\)

A car is moving with at a constant speed of \(60 \mathrm{kmh}^{-1}\) on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at distance of \(100 \mathrm{~m}\) and is approaching with a speed of \(5 \mathrm{~km} \mathrm{~h}^{-1}\). In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every \(2 \mathrm{~s}\) till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct? (a) The speed of the car in the rear is \(65 \mathrm{~km} \mathrm{~h}^{-1}\) (b) In the side mirror the car in the rear would appear to approach with a speed of \(5 \mathrm{~km} \mathrm{~h}^{-1}\) to the driver of the leading car (c) In the rear view minor, the speed of the approaching car would appeat to decrease as the distance between the. cars decreases (d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases

For a normal eye, the far point is at infinity and the near point of distinct vision is about \(25 \mathrm{~cm}\) in front of the eye. The cornea of the eye provides a converging power of about \(40 \mathrm{D}\), and the least converging power of the eye lens behind the cornea is about \(20 \mathrm{D}\). From this rough data estimate the range of accommodation (i.e., the range of converging power of the eye lens) of a normal eye. [al 10 tol4 D (b) 20 to \(24 \mathrm{D}\) (c) 28 to \(32 \mathrm{D}\) (d) 14 to \(18 \mathrm{D}\)

A ray of light travelling in glass \(\left(\mu=\frac{3}{2}\right)\) is incident on a horizontal glass air surface at the critical angle \(\theta_{c}\) If thin layer of water \(\left(\mu=\frac{4}{3}\right)\) is now poured on the glass air surface, the angle at which the ray emerges into air at the water-air surface is (a) \(60^{\circ}\) (b) \(45^{\circ}\) (c) \(\underline{90^{\circ}}\) (d) \(180^{*}\)

A beam of parallel rays is brought to a focus by a plano-convex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is (a) the focal points shifts away from the lens by a small distance (b) the focus remains undisturbed (c) the focus shifts to infinity (d) the focal points shifts towards the lens by a small distance

A photograph of the moon was taken with telescope. Later on, it was found that a housefly was sitting on the objective lens of the telescope, in photograph, (a) there is a reduction in the intensity of the image (b) there is an increase in the intensity of the image (c) the image of housefly reduced (d) the image of the housefly will be enlarged

The magnifying power of a telescope is 9. When it is adjusted for parallel rays, the distance between the objective and the eyepiece is found to be \(20 \mathrm{~cm}\). The focal lengths of the lenses are (a) \(18 \mathrm{~cm}, 2 \mathrm{~cm}\) (b) \(11 \mathrm{~cm}, 9 \mathrm{~cm}\) (c) \(10 \mathrm{~cm}, 10 \mathrm{~cm}\) (d) \(15 \mathrm{~cm}, 5 \mathrm{~cm}\)

A concave mirror and a converging lens (glass with \(\mu=1.5\) ) both have a focal length of \(3 \mathrm{~cm}\) when in air. When they are in water \(\left(\mu=\frac{4}{3}\right)\), their new focal length are (a) \(f_{\text {Lem }}=12 \mathrm{~cm}, f_{\text {sins }}=3 \mathrm{~cm}\) (b) \(f_{\text {Lens }}=3 \mathrm{~cm}, \overline{f_{\text {Miner }}}=12 \mathrm{~cm}\) (c) \(f_{\text {Lens }}=3 \mathrm{~cm}, \overline{f_{\text {Miner }}}=3 \mathrm{~cm}\) (d) \(f_{\text {Lmi }}=12 \mathrm{~cm}, f_{\text {uinar }}=12 \mathrm{~cm}\)

The focal lengths of the objective and eyelenses of a microscope are \(1.6 \mathrm{~cm}\) and \(2.5 \mathrm{~cm}\) respectively. The distance between the two lenses is \(21.7 \mathrm{~cm}\). If the final image is formed at infinity, the distance between the object the objeetive lens is (a) \(1.8 \mathrm{~cm}\) (b) \(1.70 \mathrm{~cm}\) (c) \(1.65 \mathrm{~cm}\) (d) \(1.75 \mathrm{~cm}\)

Two points, separated by a distance of \(0.1 \mathrm{~mm}\), can just be inspeeted on a microscope when light of wavelength \(6000 \AA{A}\) is used. If the light of wavelength \(4800 \dot{A}\) is used, the limit of resolution is (a) \(0.8 \mathrm{~mm}\) (b) \(0.08 \mathrm{~mm}\) (c) \(0.1 \overline{\mathrm{mm}}\) (d) \(0.04 \mathrm{~mm}\)

Consider an extended object immersed in water contained in a plane trough. When seen from close to the edge of the trough the object looks distorted because [NCERT Exemplat] (a) the apparent depth of the points dose to the edge are nearer the surface to the water compated to the points away from the edge. (b) the angle subtended by the image of the object at the eye is smaller than the actual angle subtended by the object in air (c) some of the points of the object far away from the edge may not be visible because of total internal reflection (d) water in a trough acts as a lens and magnifies the object

1 With diaphragm the camera lens set at \(f / 2\), the correct exposure times is \(1 / 100\) s. Then with diaphragm set at \(f / 8\), the correct exposure time is (a) \(1 / 100 \mathrm{~s}\) (b) \(1 / 400 \mathrm{~s}\) (c) \(1 / 200 \mathrm{~s}\) (d) \(16 / 100 \mathrm{~s}\)

There are three optical media, 1,2 and 3 with their refractive indices \(\mu_{1}>\mu_{2}>\mu_{3}\) (TIR- total internal reflection) (a) When a tay of light travels from 3 to 1 no \(\mathrm{TIR}\) will take place (b) Critical angle between \(\mid\) and 2 is less than the critical angle between \(I\) and 3 (c) Critical angle between 1 and 2 is more than the critical angle between 1 and 3 (d) Chances of 'TR are more when ray of light travels from 1 to 3 compare to the case when it travel fram 1 to 2

An object is viewed through a compound microscope and appears in focus when it is \(5 \mathrm{~mm}\) away from the objective lens. When a sheet of transparent material \(3 \mathrm{~mm}\) thick is placed between the objective and the microscope, the objective lens has to be moved \(1 \mathrm{~mm}\) to bring to object back into the focus. The refraetive index of the transparent material is (a) \(1.5\) (b) \(1.6\) (c) \(1.8\) (d) \(2.0\)

A hypermetropic person having near point at a distance of \(0.75 \mathrm{~m}\) puts on spectacles of power \(2.5 \mathrm{D}\). The near point now is at (a) \(0.75 \mathrm{~m}\) (b) \(0.83 \mathrm{~m}\) (c) \(0.36 \mathrm{~cm}\) (d) \(0.26 \mathrm{~m}\)

A ray of light travelling in a transparent medium falls on a surface separating the medium from air, at an angle of incidence of \(45^{\circ} .\) The ray undergoes total internal reflection. If \(n\) is the refractive index of the medium with respect to air, select the possible values of \(n\) from the following (a) \(1.3\) (b) \(1.4\) (c) \(1.5\) (d) \(1.60\)

An astronomical telescope has a converging eyepiece of focal length \(5 \mathrm{~cm}\) and objective of focal length \(80 \mathrm{~cm}\). When the final image is formed at the least distance of distinet vision \((25 \mathrm{~cm})\), the separation between the two lenses is (a) \(75.0 \mathrm{~cm}\) (b) \(80.0 \mathrm{~cm}\) (c) \(84.2 \mathrm{~cm}\) (d) \(85.0 \mathrm{~cm}\)

A planet is observed by an astronomical refracting telescope having an objective of focallength \(16 \mathrm{~m}\) and an eyepiece of focal length \(2 \mathrm{~cm}\) (a) The distance between the objective and the eyepiece is \(16.02 \mathrm{~m}\) (b) The angular magnification of the planct is \(-800\) (c) The image of the planet is imverted (d) The objective is larger than the eyepiece

A man's near point is \(0.5 \mathrm{~m}\) and far point is \(3 \mathrm{~m}\). Power spectacle lenses repaired for (i) reading purpose (ii) seeing distant object, respectively. (a) \(-2 \mathrm{D}\) and \(+3 \mathrm{D}\) (b) \(+2 \mathrm{D}\) and \(-3 \mathrm{D}\) (c) \(+2 \mathrm{D}\) and \(0.33 \mathrm{D}\) (d) \(-2 \mathrm{D}\) and \(+0.33 \mathrm{D}\)

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque sereen (a) Half the image will disappear (b) Complete image will be formed (c) Intensity of the image will increase (d) Intensity of the imaqe will decrease

A hypermetropie person has to use a lens of power \(+5 \mathrm{D}\) to normalise his vision. The near point of the hypermetropic eye is |al \(1 \mathrm{~m}\) (b) \(1.5 \mathrm{~m}\) (c) \(0.5 \mathrm{~m}\) (d) \(0.66 \mathrm{~m}\)

The focal length of the objective and the eyepiece of a microscope are \(4 \mathrm{~mm}\) and \(25 \mathrm{~mm}\) respectively. If the final image is formed at infinity and the length of the tube is \(16 \mathrm{~cm}\), then the magnifying power of microscope will be (a) - \(337.5\) (b) \(-3.75\) (c) \(3.375\) (d) \(33.75\)

Between the primary and secondary rainbows, there is a dark band known as Alexander's dark band. This is because (a) light scattered into this region interfere destructively (b) there is no light scattered into this region (c) light is absorbed in this region [d) angle made at the eye by the scattered rays with respect to the incident light of the sun lies between approximately \(42^{\prime \prime}\) and \(50^{\circ}\)

A simple microscope consists of a concave lens of power \(-10 \mathrm{D}\) and a convex lens of power \(+20 \mathrm{D}\) in contact. If the image is formed at infinity, then the magnifying power when \(D=25 \mathrm{~cm}\) is (a) \(2.5\) (b) \(3.5\) (c) \(2.0\) (d) \(3.0\)