Question

A plano convex lens of refractive index 1.5 and radius of curvature $$30\,cm.$$  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 object be placed in order to have a real image of size of the object

A. $$60\,cm$$
B. $$30\,cm$$
C. $$20\,cm$$  
D. $$80\,cm$$
Answer :   $$20\,cm$$
Solution :
KEY CONCEPT : The focal length $$(F)$$  of the final mirror is
$$\frac{1}{F} = \frac{2}{{{f_\ell }}} + \frac{1}{{{f_m}}}$$
$$\eqalign{ & {\text{Here, }}\frac{1}{{{f_\ell }}} = \left( {\mu - 1} \right)\left( {\frac{1}{{{R_1}}} - \frac{1}{{{R_2}}}} \right) \cr & = \left( {1.5 - 1} \right)\left[ {\frac{1}{\alpha } - \frac{1}{{ - 30}}} \right] \cr & = \frac{1}{{60}} \cr & \therefore \,\,\frac{1}{F} = 2 \times \frac{1}{{60}} + \frac{1}{{\frac{{30}}{2}}} \cr & = \frac{1}{{10}} \cr & \therefore \,\,F = 10\,cm \cr} $$
The combination acts as a converging mirror. For the object to be of the same size of mirror,
$$u = 2F = 20\,cm$$

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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