Chapter 23

A dentist has a small mirror of focal length \(16 \mathrm{~mm}\). He views the cavity in the tooth of a patient by holding the mirror at a distance of \(8 \mathrm{~mm}\) from the cavity. The magnification is (a] I (b) \(1.5\) (c) 2 (d) 3

Two point sources \(A\) and \(B\) of luminous intensities 1 od and 16 cd respectively are placed \(100 \mathrm{~cm}\) apart. A \mathrm{\\{} g r e a s e ~ s p o t ~ s e r e e n ~ i s ~ p l a c e d ~ b e t w e e n ~ t h e ~ t w o ~ s o u r c e s . ~ For the grease spot to become indistinguishable from both the sides, it should be placed at (a) \(80 \mathrm{~cm}\) from 16 cd lamp and \(20 \mathrm{~cm}\) from \(1 \mathrm{~cd}\) (b) \(20 \mathrm{~cm}\) from the \(16 \mathrm{~cd}\) and \(80 \mathrm{~cm}\) from \(1 \mathrm{~cd}\) (c) \(\frac{400}{3} \mathrm{~cm}\) from \(16 \mathrm{~cd}\) and \(\frac{100}{3} \mathrm{~cm}\) from \(1 \mathrm{~cd}\) (d) \(\frac{100}{3} \mathrm{~cm}\) from \(16 \mathrm{~cd}\) and \(\frac{400}{3} \mathrm{~cm}\) from \(1 \mathrm{~cd}\)

Given width of aperture \(=3 \mathrm{~mm}\) and \(\lambda=500 \mathrm{~nm}\). For what distance ray optics is good approximation? (a) \(18 \mathrm{~m}\) (b) \(18 \mathrm{~mm}\) (c) \(18 \bar{A}\) (d) 18 light years

A 4.5 \(\mathrm{cm}\) needle is placed \(12 \mathrm{~cm}\) away from a convex mirror of focal length \(15 \mathrm{~cm}\). Give the location of the image and the magnification. What happens as the needle is moved farther from the mirror? (a) Image goes on increasing (b) Image goes on decreasing (c) Image will be unchanged (d) Imaoe may change or channe

'The separation between the screen and a plane mirror is \(2 r\). An isotopic point source of light is placed exactly mid ways between the mirror and the screen. Assume that mirror reflects \(100 \%\) of incident light. Then the ratio of illuminance on the screen with and without the mirror is (a) \(10 ; 1\) (b) \(2: 1\) (c) \(10 ; 9\) (d) \(9: 1\)

When an object is kept at a distance of \(30 \mathrm{~cm}\) from a concave mirror, the image is formed at a distance of \(10 \mathrm{~cm}\). If the object is moved with a speed of \(9 \mathrm{~ms}^{-1}\), the speed with which images moves, is (a) \(0.1 \mathrm{~ms}^{-1}\) (b) \(1 \mathrm{~ms}^{-1}\) (c) \(3 \mathrm{~ms}^{-1}\) (d) \(9 \mathrm{~ms}^{-1}\)

An object is placed a symmetrically between two plane mirrors inclined at an angle of \(72^{\circ}\). The number of image formed is (a) 5 (b) 4 (c) 2 (d) infinite

A compound microscope has an objective and eye-piece as thin lenses of focal lengths \(1 \mathrm{em}\) and \(5 \mathrm{~cm}\) respectively. The distance between the objective and the eye-piece is \(20 \mathrm{~cm}\). The distance at which the object must be placed infront of the objective if the final image is located at \(25 \mathrm{~cm}\) from the eyepiece, is numerically (a) \(95 / 6 \mathrm{~cm}\) (b) \(5 \mathrm{~cm}\) (c) \(95 / 89 \mathrm{~cm}\) (d) \(25 / 6 \mathrm{~cm}\)

A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ}\), then the fish could see things above water surface within an angular range of \(\theta^{\circ}\) where (a) \(\theta=49^{\circ}\) (b) \(\theta=98^{\circ}\) (c) \(\theta=24 \frac{1}{4}\) [d) \(\theta=90^{\circ}\)

An object is placed \(30 \mathrm{em}\) to the left of a diverging lens whose focal length is of magnitude \(20 \mathrm{~cm}\). Which one of the following correctly states the nature and position of the virtual image formed? \(\begin{array}{ll}\text { Nature of image } & \text { Distance from lens }\end{array}\) (a) inverted enlarged \(60 \mathrm{~cm}\) to the right (b) erect, diminished \(12 \mathrm{~cm}\) to the left (c) irverted, enlarged \(60 \mathrm{~cm}\) to the left \(\begin{array}{ll}\text { (d) erect, diminished } & 12 \mathrm{~cm} \text { to the right }\end{array}\) (c) imverted, enlarged \(12 \mathrm{~cm}\) to the left

A car is fitted with a convex mirror of focal length \(20 \mathrm{~cm}\). A second car \(2 \mathrm{~m}\) broad and \(1.6 \mathrm{~m}\) height is \(6 \mathrm{~cm}\) away from the first car. The position of the second car as seen in the mirror of the first car is (a) \(19.35 \mathrm{~cm}\) (b) \(17.45 \mathrm{~cm}\) (c) \(21,48 \mathrm{~cm}\) (d) \(15.49 \mathrm{~cm}\)

A convex mirror forms an image one-fourth the size of the object. If object is at a distance of \(0.5 \mathrm{~m}\) from the mirror, the focal length of mirror is (a) \(0.17 \mathrm{~m}\) (b) \(-1.5 \mathrm{~m}\) (c) \(0.4 \mathrm{~m}\) (d) \(-0.4 \mathrm{~m}\)

A person of 6 feet in length can see his full size erect image in a mirror 2 feet in height. This mirror has to be (a) plane or comex (b) plane or concave (c) necessarly convex (d) necessarily concave

A ray light passes through an equilateral prism such that the angle of incidence and the angle of emergence are both equal to \(3 / 4\) th of the angle of prism. The angle of minimum deviation is (a) \(15^{\circ}\) (b) \(30^{\circ}\) (c) \(45^{\circ}\) (d) \(60^{\circ}\)

A point object is placed at a distance of \(30 \mathrm{~cm}\) from a convex mirror of a focal length \(30 \mathrm{~cm}\). The image will form at [al infinity (b) pole (c) \(15 \mathrm{~cm}\) behind the mirrot (d) no image will be formed

A plane mirror is reflecting a ray of incident light is rotated through an angle of about an axis through the point of incidence in the plane of the mirror perpendicular to the plane of incident, then (a) the reflected ray rotates through an angle \(2 \theta\) (b) the reflected ray rotates through an angle of \(\theta\) (c) the reflected ray does not rotate (d) None of the above

A thin equiconvex lens of refractive index \(3 / 2\) and radius of curvature \(30 \mathrm{~m}\) is put in water (refractive index \(=\frac{4}{3}\). Its focal length is (a) \(0.15 \mathrm{~m}\) (b) \(0.30 \mathrm{~m}\) (c) \(0.45 \mathrm{~m}\) (d) \(1.20 \mathrm{~m}\)

A man has a concave shaving mirror or focal length \(0.2 \mathrm{~m}\). How far should the mirror be held from his face in order to give an image of two fold magnification? (a) \(-0.1 \mathrm{~m}\) (b) \(0.2 \mathrm{~m}\) (c) \(0.3 \mathrm{~m}\) (d) \(0.4 \mathrm{~m}\)

Two lenses, one concave and the other convex of same power are placed such that their principal axes coincide. If the separation between the lenses is \(x\), then (a) real image is formed for \(x=0\) only (b) real image is formed for all values of \(x\) (c) system will behave like a glass plate for \(x=0\) (d) virtual image is formed for all values of \(x\) other than zero

To focal length of a concave mirror is \(12 \mathrm{~cm}\). Where should an object of length \(4 \mathrm{~cm}\) be placed so that an image \(1 \mathrm{~cm}\) long is formed? (a) \(48 \mathrm{~cm}\) (b) \(3 \mathrm{~cm}\) (c) \(-60 \mathrm{~cm}\) (d) \(15 \mathrm{~cm}\)

A ray of light falls on a transparent glass slab with refractive index (relative to air) of \(1.62 .\) The angle of incidence for which the reflected and refracted rays are mutually perpendicular is (a) \(\tan ^{-1}(162)\) (b) \(\sin ^{-1}(162)\) (c) \(\cos ^{-1}(162)\) (d) None of these

A double convex lens made out of glass (refractive index, \(\mu=15\) ) has both radii of curvature of magnitudes \(20 \mathrm{~cm}\). Incident light rays parallel to the axis of this lens will converge at a distance, \(d\) such that (a) \(d=10 \mathrm{~cm}\) (b) \(d=\frac{20}{3} \mathrm{~cm}\) (c) \(d=40 \mathrm{~cm}\) (d) \(d=20 \mathrm{~cm}\)

A spherical mirror forms diminished virtual image of magnification \(1 / 3 .\) Focal length is \(18 \mathrm{~cm}\). The distance of the object is (a) \(18 \mathrm{~cm}\) (b) \(-36 \mathrm{~cm}\) (c) \(48 \mathrm{~cm}\) (d) infinite

Sun subtends an angle of \(0.5^{\circ}\) at the centre of curvature of a concave mirror of radius of curvature \(15 \mathrm{~m}\). The diameter of the image of the sun formed by the mirror is (a) \(8.55 \mathrm{~cm}\) (b) \(7.55 \mathrm{~cm}\) (c) \(6.55 \mathrm{~cm}\) (d) \(6.55 \mathrm{~cm}\)

A thin lens has focal length, \(f_{1}\) and its aparture has diameter \(d\). It forms an image of intensity \(I .\) Now the central part of the aparture upto diameter \(\frac{d}{2}\) is blocked by an opaque paper. The focal length and image intensity will be change to (a) \(f\) and \(\frac{1}{4}\) (b) \(f\) and \(\frac{3 l}{4}\) (c) \(\frac{f}{2} \operatorname{and} \frac{l}{2}\) (d) \(\frac{3 f}{4}\) and \(\frac{1}{2}\)

A small candle, \(2.5 \mathrm{~cm}\) in size is placed at \(27 \mathrm{~cm}\) in front of a concave mirror of radius of curvature \(36 \mathrm{~cm}\). At what distance from the mirror should a sereen be placed in order to obtain a sharp image? Deseribe the nature and size of the image. If the candle is moved closer to the mirror, how would the sereen have to be moved? (a) \(54 \mathrm{~cm}\) (b) \(27 \mathrm{~cm}\) (c) \(28 \mathrm{~cm}\) (d) \(475 \mathrm{~cm}\)

An object \(5 \mathrm{~cm}\) tall is placed \(1 \mathrm{~m}\) from a concave spherical mirror which has a radius of curvature of \(20 \mathrm{~cm}\). The size of the image is (a) \(0.11 \mathrm{~cm}\) (b) \(-0.55 \mathrm{~cm}\) (c) \(0.55 \mathrm{~cm}\) (d) \(0.60 \mathrm{~cm}\)

An convex mirror of radius of curvature \(1.6 \mathrm{~m}\) has an object placed at a distance of \(1 \mathrm{~m}\) from it. The image is formed at a distance of (a) \(8 / 13 \mathrm{~m}\) in front of the mirror (b) \(8 / 13 \mathrm{~m}\) behind the mirror (c) \(4 / 9 \mathrm{~m}\) in front of the mirror (d) \(4 / 9 \mathrm{~m}\) behind the mirror

A beam of electrons is used in a YDSE experiment to slit width is \(d\), when the velocity of electrons is increased, then (a) no interference is observed (b) fringe width increases (c) fringe width decreases (d) fringe width remains same

In the Young's double slit experiment, the central maxima in observed to be \(I_{0}\). If one of the slits is covered, then the intensity at the central maxima will become (a) \(\frac{l_{0}}{2}\) (b) \(\frac{l_{0}}{\sqrt{2}}\) (c) \(\frac{l_{0}}{=}\) (d) \(\overline{I_{0}}\)

A plane mirror is approaching you at \(10 \mathrm{cms}^{-1}\). Your image shall approach you with a speed of (a) \(+10 \mathrm{cms}^{-1}\) (b) \(-10 \mathrm{cms}^{-1}\) (c) \(+20 \mathrm{cms}^{-1}\) (d) \(-20 \mathrm{cms}^{-1}\)

A convex lens and a concave lens each having same focal length of \(25 \mathrm{~cm}\) are put in contact of a combination of lenses. The power of the combination is (a) zero (b) infinite (c) 100 (d) 10

The dispersive power of the material of lens of foeal length \(20 \mathrm{~cm}\) is \(0.08 .\) The longitudinal chromatic aberration in of the lens is [a) \(0.08 \mathrm{~cm}\) (b) \(1.6 \mathrm{~cm}\) (c) \(0.8 \mathrm{~cm}\) (d) \(0.16 \mathrm{~cm}\)

An object is approaching a plane mirror at \(10 \mathrm{cms}^{-1} .\) A stationary observer sees the image. At what speed will the image approach the stationary observer? (a) \(10 \mathrm{cms}\) (b) \(5 \mathrm{cms}^{-1}\) (c) \(20 \mathrm{cms}^{-1}\) (d) \(15 \mathrm{cms}^{-1}\)

A small objeet is placed \(10 \mathrm{~cm}\) in front of a plane mirror. If you stand behind the object, \(30 \mathrm{~cm}\) from the mirror and look at its image, for what distance must you focus your eyes? (a) \(20 \mathrm{~cm}\) (b) \(60 \mathrm{~cm}\) (c) \(80 \mathrm{~cm}\) (d) \(40 \mathrm{~cm}\)

A ray of light makes an angle of \(10^{\circ}\) with the horizontal above it and strikes a plane mirror which is inclined at an angle \(\theta\) to the horizontal. The angle \(\theta\) for which the reflected ray becomes vertical is (a) \(50^{*}\) (b) \(80^{*}\) (c) \(100^{\circ}\) (d) \(4 \overline{0^{*}}\)

When a convergent beam of light is incident on a plane mirror, the image formed is (a) upright and real (b) upright and virtual [c) inverted and virtual (d) irverted and real

A telescope has an objective of focal length \(50 \mathrm{~cm}\) and an eyepiece of focal length \(5 \mathrm{~cm}\). The least distance of distinct vision is \(25 \mathrm{~cm}\). The telescope is focussed for distinct vision on a scale \(200 \mathrm{~cm}\) away. The separation between the objective and eyepiece is (a) \(74 \mathrm{~cm}\) (b) \(75 \mathrm{~cm}\) (c) \(60 \mathrm{~cm}\) (d) \(71 \mathrm{~cm}\)

It is necessary to illuminate the bottom of a well by reflected solar beam when the light is incident at an angle of \(\alpha=40^{\circ}\) to the vertical. At what angle \(\beta\) to the horizontal should a plane mirror be placed? (a) \(70^{\circ}\) (b) \(20^{*}\) (c) \(50^{\circ}\) (d) \(40^{\circ}\)

The sun (diameter \(d\) ) subtends an angle \(\theta\) radian at the pole of a concave mirror of foeal length \(f\). The diameter of the image of sun formed by mirror (a) \(\underline{\theta f}\) (b) \(\frac{\theta}{2} f\) (c) \(29 \mathrm{f}\) (d) \(\frac{\theta}{\pi} f\).

At what angle should a ray of light be incident on the face of a prism of refracting angle \(60^{\circ}\) so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is \(1.524\). [NCERT] (a) \(16^{\circ}\) (b) \(29^{\circ}\) (c) \(45^{\circ}\) (d) \(58^{\circ}\)

A spherical mirror forms an image of magnification \(m=\pm 3 .\) The object distance, if focal length of mirror is \(24 \mathrm{~cm}\), may be (a) \(32 \mathrm{~cm}, 24 \mathrm{~cm}\) (b) \(32 \mathrm{~cm}, 16 \mathrm{~cm}\) (c) \(32 \mathrm{~cm}\) only (d) \(16 \mathrm{~cm}\) only

A thin plano-convex lens focal length \(f\) is split into two halves. One of the halves is shifted along the optical axis. The separation between object and image plane is \(1.8 \mathrm{~m}\). The magnification of the image formed by one of the halflens is 2. Find the focal- length of the lens and separation between the two halves. (a) \(0.1 \mathrm{~m}\) (b) \(0.4 \mathrm{~m}\) (c) \(0.9 \mathrm{~m}\) (d) \(1 \mathrm{~m}\)

A plano-convex lens has a thickness of \(4 \mathrm{~cm}\). When placed on a horizontal table, with the curved surface in contact with it, the apparent depth of the bottom most point of the lens is found to be \(3 \mathrm{~cm}\). If the lens is inverted such that the plane face is in contact with the table, the apparent depth of the centre of the plane face is found to be \(25 / 8 \mathrm{~cm}\). Find the foeal length of the lens. Assume thickness to be negligible (a) \(85 \mathrm{~cm}\) (b) \(59 \mathrm{~cm}\) (c) \(75 \mathrm{~cm}\) (d) \(7.5 \mathrm{~cm}\)

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

Two convex lenses placed in contaet form the image of a distance object at \(P .\) If the lens \(B\) is moved to the right, the image will (a) move to the left (b) move to the right (c) remain at \(P\) (d) move either to the left or right, depending upon focal Icngth of the lenses

A ray of light from a denser medium strikes a rarer medium at angle of incidence \(\angle\) The reflected and refracted rays make an angle of \(90^{\circ}\) with each other. The angles of reflection and refraction are \(r\) and \(r^{\prime}\) respectively. The critical angle is (a) \(\sin ^{-1}\left(\tan r^{*}\right)\) (b) \(\sin ^{-1}(\tan r)\) (c) \(\tan ^{-1}\left(\tan t^{\prime}\right)\) (d) \(\tan ^{-1}(\tan i]\)

If eye is kept at a depth \(h\) inside water of refractive index and viewed outaide, then the diameter of the cirele through which the outer objects become visible, will be (a) \(\frac{h}{\sqrt{\mu^{2}-1}}\) (b) \(\frac{h}{\sqrt{\mu_{2}+1}}\) (c) \(\frac{2 h}{\sqrt{\mu^{2}-1}}\) (d) \(\frac{h}{\sqrt{\mu^{2}}}\)

A small bulb is placed at the bottom of a tank containing water to a depth of \(80 \mathrm{~cm}\). What is the area of the surface of water through which light from the bulb ean emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.) [NCERT] (a) \(4.6 \mathrm{~m}^{2}\) (b) \(3.2 \mathrm{~m}\) (c) \(5.6 \mathrm{~m}^{2}\) (d) \(2.6 \mathrm{~m}^{2}\)

A convex lens \(A\) of focal length \(20 \mathrm{~cm}\) and a concave lens \(B\) of focal length \(56 \mathrm{~cm}\) are kept along the same axis with the distance \(d\) between them. If a parallel beam of light falling on \(A\) leaves \(B\) as a parallel beam, beam then distance, \(d\) in \(\mathrm{cm}\), will be (a) 25 (b) 36 (c) 30 (d) 50