Chapter 20

Due to increase of temperature of medium, refractive index will be: (a) decreased (b) increased (c) unchanged (d) none of these

In the case of refraction: (a) the frequency of light changes (b) the phase changes (c) the wave length changes (d) all the above

The rising and setting of sun appear red because of : (a) refraction (b) reflection (c) diffraction (d) scattering

The electric permittivity and magnetic permeability of free space are \(\varepsilon_{0}\) and \(\mu_{0}\), respectively. The index of refraction of the medium, if \(\varepsilon\) and \(\mu\) are the electric permittivity and magnetic permeability in a medium is : (a) \(\frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}}\) (b) \(\left(\frac{\varepsilon \mu}{\varepsilon_{0} \mu_{0}}\right)^{1 / 2}\) (c) \(\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}\) (d) \(\left(\frac{\varepsilon_{0} \mu_{0}}{\varepsilon \mu}\right)^{1 / 2}\)

The maximum possible deviation of the ray, when a ray of light travels from an optically denser to rarer medium and the critical angle for the two medium is \(C\), is : (a) \((\pi-C)\) (b) \((\pi-2 C)\) (c) \(2 C\) (d) \(\left(\frac{\pi}{2}+C\right)\)

A ray of light falls on a transparent glass slab of refractive index 1.62. What is the angle of incidence, if the reflected ray and refracted ray are mutually perpendicular? (a) \(\tan ^{-1}(1.62)\) (b) \(\tan ^{-1}\left(\frac{1}{1.62}\right)\) (c) \(\frac{1}{\tan ^{-1}(1.62)}\) (d) None of these

In a medium of refractive index \(n_{1}\), a monochromatic light of wavelength \(\lambda_{1}\) is travelling. When it enters in a denser medium of refractive index \(n_{2}\), the wavelength of the light in the second medium is : (a) \(\lambda_{1}\left(\frac{n_{1}}{n_{2}}\right)\) (b) \(\lambda_{1}\left(\frac{n_{2}}{n_{1}}\right)\) (c) \(\frac{\lambda_{1}\left(n_{2}-n_{1}\right)}{n_{2}}\) (d) \(\frac{\lambda_{1}\left(n_{2} \cdots n_{1}\right)}{n_{1}}\)

The focal lengths of a thin convex lens for red and violet colours are \(44.6 \mathrm{~cm}\) and \(42.5 \mathrm{~cm}\). The focal length for the mean colour and dispersive power of the lens are respectively: (a) focal length \(=43.53 \mathrm{~cm}\) dispersive power \(=0.048\) (b) focal length \(=28.53\) dispersive power \(=0.048\) (c) focal length \(=63.53 \mathrm{~cm}\) dispersive power \(=8.48\) (d) focal length \(=30.43\) dispersive power \(=4.8\)

\(x-y\) plane separates two media. \(z>0\) contains a medium of refractive index 1 and \(z<0\) contains a medium of refractive index \(2 .\) A ray of light is incident from first medium along a vector \(\hat{i}+\hat{j}-\hat{k}\), the unit vector along refracted ray is : (a) \(\frac{1}{2 \sqrt{3}} \hat{\mathbf{i}}+\frac{1}{2 \sqrt{3}} \hat{\mathbf{j}}-\sqrt{\frac{5}{6}}^{-}\) (b) \(\frac{1}{2 \sqrt{3}} \hat{\mathbf{i}}+\frac{1}{2 \sqrt{3}} \hat{\imath}-\frac{1}{2 \sqrt{3}} \hat{k}\) (c) \(\hat{i}+\vec{j}-\hat{k}\) (d) none of the above

A light ray strikes a flat glass plate, at a small angle ' \(\theta^{\prime}\). The glass plate has thickness ' \(t\) ' and refractive index ' \(\mu^{\prime}\). What is the lateral displacement ' \(d^{\prime}\) ? (a) \(\frac{t \theta(\mu+1)}{\mu}\) (b) \(\frac{t \theta(\mu-1)}{\mu}\) (c) \(\frac{t}{\theta \mu}(\mu-1)\) (d) \(\frac{\mu}{t \theta}(\mu+1)\)

A tank contains two different liquids which do not mix with each other. The lower and upper liquids are at depth \(h_{2}\) and \(h_{1}\) respectively and of refractive indices \(\mu_{2}\) and \(\mu_{1}\). An object ' \(O^{\prime}\) is located at the bottom, when seen vertically from above. Locate the position of image of the object \(O\) as seen from above : (a) \(\frac{h_{1}}{\mu_{1}}-\frac{h_{2}}{\mu_{2}}\) (b) \(\frac{h_{1}}{\mu_{1}}+\frac{h_{2}}{\mu_{2}}\) (c) \(\frac{h_{1}}{\mu_{2}}+\frac{h_{2}}{\mu_{1}}\) (d) \(\frac{h_{1}}{\mu_{2}}-\frac{h_{2}}{\mu_{1}}\)

A vessel contains a slab of glass \(8 \mathrm{~cm}\) thick and of refractive index 1.6. Over the slab, the vessel is filled by oil of refractive index \(\mu\) upto height \(4.5 \mathrm{~cm}\) and also by another liquid i.e., water of refractive index \(4 / 3\) and height \(6 \mathrm{~cm}\) as shown in figure. An observer lookingdown from above, observes that, a mark at the bottom of the glass slab appears to be raised up to position \(6 \mathrm{~cm}\) from the bottom of the slab. The refractive index of oil \((\mu)\) is: (a) \(1.5\) (b) \(2.5\) (c) \(0.5\) (d) \(1.2\)

\(n\) transparent slabs of refractive index \(1.5\) each having thickness \(1 \mathrm{~cm}, 2 \mathrm{~cm}, \ldots\) to \(n \mathrm{~cm}\) are arranged one over another. A point object is seen through this combination with near perpendicular light. If the shift of object by the combination is \(1 \mathrm{~cm}\) then the value of \(n\) is: (a) either 2 or 3 (b) 2 (c) 3 (d) \(0.3\)

In the figure, a point source \(' P^{\prime}\) is placed at a height \(h\) above the plane mirror in a medium of refractive index \(\mu\). An observer \(O\), vertically above \(P\), outside the liquid, sees \(P\) and its image in the mirror. The apparent distance between these two is: (a) \(2 \mu h\) (b) \(\frac{2 h}{\mu}\) (c) \(\frac{2 h}{\mu-1}\) (d) \(h\left(1+\frac{1}{\mu}\right)\)

In a lake, a fish rising vertically to the surface of water uniformly at the rate of \(3 \mathrm{~m} / \mathrm{s}\), observes a bird diving vertically towards the water at a rate of \(9 \mathrm{~m} / \mathrm{s}\) vertically above it. The actual velocity of the dive of the bird is: (Given: refractive index of water \(=4 / 3\) ) (a) \(9.2 \mathrm{~m} / \mathrm{s}\) (b) \(4.5 \mathrm{~m} / \mathrm{s}\) (c) \(9.0 \mathrm{~m} / \mathrm{s}\) (d) \(3.2 \mathrm{~m} / \mathrm{s}\)

A concave mirror with its optic axis vertical and mirror facing upward is placed at the bottom of the water tank. The radius of curvature of mirror is \(40 \mathrm{~cm}\) and refractive index for water \(\mu=4 / 3\). The tank is \(20 \mathrm{~cm}\) deep and if a bird is flying over the tank at a height \(60 \mathrm{~cm}\) above the surface of water, the position of image of a bird is: (a) \(3.75 \mathrm{~cm}\) (b) \(4.23 \mathrm{~cm}\) (c) \(5.2 \mathrm{~cm}\) (d) \(3.2 \mathrm{~cm}\)

Word 'Newton' is printed on a paper and is placed on a horizontal surface below a cubical glass. The minimum value of refractive index of a cubical glass for whichletters are not visible from any of vertical faces of the glass, is: (a) \(\sqrt{3}\) (b) \(0.5\) (c) 1 (d) \(\sqrt{2}\)

In a tank filled with water of refractive index \(5 / 3\), a point source of light is placed \(4 \mathrm{~m}\) below the surface of water. To cut-off all light coming out of water from the source, what should be the minimum diameter of a disc, which should be placed over the source on the surface of water ? (a) \(1 \mathrm{~m}\) (b) \(4 \mathrm{~m}\) (c) \(3 \mathrm{~m}\) (d) \(6 \mathrm{~m}\)

In a prism a ray deviates towards: (a) base of prism (b) refracting edge of a prism (c) normal to the base (d) second phase of the prism

A glass prism of refractive index \(8 / 5\) is immersed in a liquid of refractive index \(4 / 3 .\) A ray of light incident at grazing angle on one face emerges at grazing angle on the other face of the prism. The angle of the prism is : (a) \(30^{\circ}\) (b) \(60^{\circ}\) (c) \(37^{\circ}\) (d) none of these

An equilateral prism deviates a ray through \(45^{\circ}\) for the two angle of incidence differing by \(20^{\circ}\). The angle of incidence is: (a) \(60^{\circ}\) (b) \(40^{\circ}\) (c) \(120^{\circ}\) (d) none of these

There is a glass prism of refractive index \(\mu\) and angle of prism is \(A\). A ray of light enter the side \(A B\) face of the prism at an angle of incidence \(i\). The value of angle of incidence \(i\) so, that no ray emerges from the face \(A C\) of the prism, is: (a) \(\sin ^{-1}\left[\sqrt{\mu^{2}-1} \sin A-\cos A\right]\) (b) \(\sin ^{-1}\left[\sqrt{\mu^{2}+1} \sin A-\cos A\right]\) (c) \(\sin ^{-1}\left[\sqrt{\mu^{2}+1} \sin A+\cos A\right]\) (d) none of the above

The refractive index of the material of prism, if a thin prism of angle \(A=6^{\circ}\), produces a deviation \(\delta=3^{\circ}\), is: (a) \(1.5\) (b) \(1.2\) (c) \(1.1\) (d) \(1.25\)

The refractive index of the material, if a prism having an angle \(A=60^{\circ}\) which produces a minimum deviation of \(30^{\circ} ?\) (a) \(\sqrt{3}\) (b) \(\sqrt{2}\) (c) \(\sqrt{5}\) (d) \(1 / \sqrt{2}\)

One face \(A C\) of the glass prism is silvered as shown and the principal section of a glass prism is an isosceles triangle \(A B C\) with \(A B=A C\). The \(\angle B A C\), if the ray incident normally on face \(A B\) and after two reflections, it emerges from the base \(B C\), perpendicular to it, is : (a) \(70^{\circ}\) (b) \(36^{\circ}\) (c) \(72^{\circ}\) (d) \(44^{\circ}\)

In a glass prism, spectrum is produced due to: (a) refraction (b) dispersion (c) scattering (d) diffraction

If a crown glass prism of refracting angle \(10^{\circ}\) have refractive indices for red and violet rays \(1.514\) and \(1.523\) respectively, then the dispersion caused by a crown glass prism is : (a) \(0.07^{\circ}\) (b) \(0.08^{\circ}\) (c) \(0.09^{\circ}\) (d) \(0.10^{\circ}\)

A thin prism of angle \(7^{\circ}\) made of glass of refractive index \(1.5\) is combined with another prism made of glass of \(\mu=1.75\) to produce dispersion without deviation. The angle of second prism is: (a) \(7^{\circ}\) (b) \(4.67^{\circ}\) (c) \(9^{\circ}\) (d) \(5^{\circ}\)

The human eye can be regarded as a single spherical refractive surface of curvature of cornea \(7.8 \mathrm{~mm}\). If a parallel beam of light comes to focus at \(3.075 \mathrm{~cm}\) behind the refractive surface, the refractive index of the eye is: (a) \(1.34\) (b) 1 (c) \(1.5\) (d) \(1.33\)

In a glass sphere, there is a small bubble \(2 \times 10^{-2} \mathrm{~m}\) from its centre. If the bubble is viewed along a diameter of the sphere, from the side on which it lies, how far from the surface will it appear? The radius of glass sphere is \(5 \times 10^{-2} \mathrm{~m}\) and refractive index of glass is \(1.5:\) (a) \(2.5 \times 10^{-2} \mathrm{~m}\) (b) \(3.2 \times 10^{-2} \mathrm{~m}\) (c) \(6.5 \times 10^{-2} \mathrm{~m}\) (d) \(0.2 \times 10^{-2} \mathrm{~m}\)

Which of the following statements is/are correct? (a) The lens has two principal foci, but may have one focal length (b) A single lens can never bring a beam of white light to a point focus (c) A burning glass brings light rays to same focus as heat radiation (d) Both (a) and (b) are correct

If the resolution limit of the eye is 1 minute and at a distance \(x \mathrm{~km}\) from the eye, two persons stand with a leteral separation of 3 metre, then the value of \(x\) for which the positions of the two persons can be just resolved by the nacked eye, is: (a) \(10 \mathrm{~km}\) (b) \(15 \mathrm{~km}\) (c) \(20 \mathrm{~km}\) (d) \(30 \mathrm{~km}\)

Select the correct alternative(s): (a) A convex lens may form a real image (b) \(R=2 f\) formula is applicable to only paraxial ray (c) A convex lens becomes less convergent when it is immersed in water (d) All of the above

From an air craft flying at an altitude of \(2000 \mathrm{~m}\), photograph of the ground are taken from a camera, whose size of the film is \(18 \mathrm{~cm} \times 18 \mathrm{~cm}\) and the focal length of camera is \(50 \mathrm{~cm}\). The area of the ground can be photographed by the camera is : (a) \(648910 \mathrm{~m}^{2}\) (b) \(721879 \mathrm{~m}^{2}\) (c) \(518400 \mathrm{~m}^{2}\) (d) \(482529 \mathrm{~m}^{2}\)

The distance between the object and screen is \(x\) and a convex lens is placed somewhere in between an object and a screen. The focal length \((f)\) of the lens, if the numerical value of magnification produced by the lens is \(m\) is : (a) \(\frac{m x}{(m+1)^{2}}\) (b) \(\frac{m x}{(m-1)^{2}}\) (c) \(\frac{(m+1)^{2}}{m} \cdot x\) (d) \(\frac{(m-1)^{2}}{m} \cdot x\)

On the axis of a spherical mirror of focal length \(f\), a short linear object of length \(L\) lies on the axis at a distance \(u\) from the mirror. Its image has an axial length \(L^{\prime}\) equal to: (a) \(L\left[\frac{f}{(u-f)}\right]^{1 / 2}\) (b) \(L\left[\frac{(u+f)}{f}\right]^{1 / 2}\) (c) \(L\left[\frac{(u-f)}{f}\right]^{2}\) (d) \(L\left[\frac{f}{(u-f)}\right]^{2}\)

The refractive index of a lens material is \(\mu\) and focal length \(f\). Due to some chemical changes in the material, its refractive index has increased by \(2 \%\). The percentage decrease, in focal length for \(\mu=1.5\) will be : (a) \(4 \%\) (b) \(2 \%\) (c) \(6 \%\) (d) \(8 \%\)

The focal length of a convex lens when placed in air and then in water will: (a) increase in water with respect to air (b) increase in air with respect to water (c) decrease in water with respect to air (d) remain the same

A lens forms a sharp image of a real object on a screen. On inserting a parallel slide between the lens and the screen with its thickness along the principal axis of the lens, it is found necessary to shift the screen parallel to itself distance \(d\) away from the lens for getting image sharply focussed on it. If the refractive index of the glass relative to air is \(\mu\), the thickness of the slab is: (a) \(\frac{d}{\mu}\) (b) \(\mu d\) (c) \(\frac{r d}{\mu-1}\) (d) \((\mu-1) \frac{d}{\mu}\)

The radius of curvature of the face of planoconvex lens is \(12 \mathrm{~cm}\) and its refractive index is \(1.5\). If the plane surface of the lens is now silvered, then the focal length of the lens is : (a) \(26 \mathrm{~cm}\) (b) \(22 \mathrm{~cm}\) (c) \(24 \mathrm{~cm}\) (d) \(20 \mathrm{~cm}\)

The change in the focal length of the lens, if a convex lens of focal length \(20 \mathrm{~cm}\) and refractive index \(1.5\), is immersed in water having refractive index \(1.33\), is : (a) \(62.2 \mathrm{~cm}\) (b) \(5.82 \mathrm{~cm}\) (c) \(58.2 \mathrm{~cm}\) (d) \(6.22 \mathrm{~cm}\)

A converging lens is used to form an image on a screen. When the upper half of the lens is covered by an opaque screen: (a) the complete image will be formed (b) the intensity of image will increase (c) the intensity of image will decrease (d) both (a) and (c) are correct

If an equiconvex lens of focal length \(30 \mathrm{~cm}\) is cut into two equal parts by a horizontal plane, then: (a) the light transmitting area of each part becomes half of the initial (b) the intensity will reduce to half (c) the aperture becomes \(\frac{1}{\sqrt{2}}\) times of tis initial value (d) all the above

If an equiconvex lens of focal length \(20 \mathrm{~cm}\) is cut into two equal parts by a vertical plane, the focal length of each part will become: (a) \(40 \mathrm{~cm}\) (b) \(10 \mathrm{~cm}\) (c) \(20 \mathrm{~cm}\) (d) \(5 \mathrm{~cm}\)

Mark correct option or options: (a) The image formed by a convex lens may coincide with object (b) The image formed by a plane mirror is always virtual (c) If one surface of convex lens is silvered, then the image may coincide with the object (d) Both (a) and (b) are correct

The object distance \(u\) for a concave mirror: (a) must be positive (b) must be negative (c) must not be negative (d) may be negative

Two thin convex lenses of focal lengths \(f_{1}\) and \(f_{2}\) are separated by a horizontal distance \(d\) (where \(d

The focal length of plano-convex lens, the convex surface of which is silvered is \(0.3 \mathrm{~m}\). If \(\mu\) of the lens is \(7 / 4\), the radius of curvature of the convex surface is : (a) \(0.45 \mathrm{~m}\) (b) \(1.05 \mathrm{~m}\) (c) \(3 \mathrm{~m}\) (d) \(0.9 \mathrm{~m}\)

The focal length of the objective of a compound microscope is \(f_{o}\) and its distance from the eye piece is \(L\). The object is placed at a distance \(u\) from the objective. For proper working of the instrument: (a) \(L>u\) (b) \(L2 f_{o}\)

The magnification of a compound microscope is 30 and the focal length of its eye piece is \(5 \mathrm{~cm}\). The magnification produced by the objective, when the image is to be formed at least distance of distinct vision \((25 \mathrm{~cm})\), is: (a) 5 (b) 6 (c) 8 (d) 10