Question

An object is moving with speed $${v_0}$$ towards a spherical mirror with radius of curvature $$R,$$ along the central axis of the mirror. The speed of the image with respect to the mirror is ($$U$$ is the distance of the object from mirror at any given time $$t$$)

A. $$ + \left( {\frac{R}{{U - 2R}}} \right)v_0^2$$
B. $$ - {\left( {\frac{R}{{R - 2U}}} \right)^2}{v_0}$$  
C. $$ - {\left( {\frac{R}{{2U - 2R}}} \right)^2}{v_0}$$
D. $$ + \left( {\frac{R}{{2U - 2}}} \right)v_0^2$$
Answer :   $$ - {\left( {\frac{R}{{R - 2U}}} \right)^2}{v_0}$$
Solution :
For concave mirror
$$\eqalign{ & \frac{2}{R} = \frac{1}{v} + \frac{1}{u}\,\,{\text{or}}\,\,\frac{2}{{ - R}} = \frac{1}{v} + \frac{1}{{ - u}} \cr & \therefore \frac{1}{v} = \frac{1}{U} - \frac{2}{R} = \frac{{R - 2U}}{{UR}} \cr & {\text{or}}\,\,v = \left[ {\frac{{RU}}{{R - 2U}}} \right] \cr} $$
In spherical mirror, image velocity
$${v_i} = - \left[ {\frac{{{v^2}}}{{{u^2}}}} \right]{v_0} = - {\left[ {\frac{{RU}}{{R - 2U}}} \right]^2}\frac{{{v_0}}}{{{U^2}}} = - {\left[ {\frac{R}{{R - 2U}}} \right]^2}{v_0}$$

Releted MCQ Question on
Optics and Wave >> Ray Optics

Releted Question 1

When a ray of light enters a glass slab from air,

A. Its wavelength decreases.
B. Its wavelength increases.
C. Its frequency decreases.
D. neither its wavelength nor its frequency changes.
Releted Question 2

A glass prism of refractive index 1.5 is immersed in water (refractive index $$\frac{4}{3}$$ ). A light beam incident normally on the face $$AB$$  is totally reflected to reach on the face $$BC$$  if
Ray Optics mcq question image

A. $$\sin \theta \geqslant \frac{8}{9}$$
B. $$\frac{2}{3} < \sin \theta < \frac{8}{9}$$
C. $$\sin \theta \leqslant \frac{2}{3}$$
D. None of these
Releted Question 3

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
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A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$
Releted Question 4

A ray of light from a denser medium strike a rarer medium at an angle of incidence $$i$$ (see Fig). The reflected and retracted rays make an angle of $${{{90}^ \circ }}$$ with each other. The angles of reflection and refraction are $$r$$ and $$r’$$ The critical angle is
Ray Optics mcq question image

A. $${\sin ^{ - 1}}\left( {\tan r} \right)$$
B. $${\sin ^{ - 1}}\left( {\tan i} \right)$$
C. $${\sin ^{ - 1}}\left( {\tan r'} \right)$$
D. $${\tan ^{ - 1}}\left( {\sin i} \right)$$

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