Question

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $$40\,cm.$$  The area of the image is 9 times that of the square. The focal length of the lens is :

A. $$36\,cm$$
B. $$27\,cm$$
C. $$60\,cm$$
D. $$30\,cm$$  
Answer :   $$30\,cm$$
Solution :
If side of object square $$ = \ell $$
and side of image square $$ = \ell '$$
From question, $$\frac{{\ell '}}{\ell } = 9\,\,{\text{or}}\,\,\frac{{\ell '}}{\ell } = 3$$
i.e, magnification $$m = 3$$
$$u = - 40\,cm$$
$$v = 3 \times 40 = 120\,cm\,f = ?$$
From formula, $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
$$\eqalign{ & \frac{1}{{120}} - \frac{1}{{ - 40}} = \frac{1}{f}\,\,{\text{or,}}\,\,\frac{1}{f} = \frac{1}{{120}} + \frac{1}{{40}} = \frac{{1 + 3}}{{120}} \cr & \therefore f = 30\,cm \cr} $$

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
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. $${\tan ^{ - 1}}\left( {\sin i} \right)$$
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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