Question

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $$10\,cm.$$  The diameter of the sun is $$1.39 \times {10^9}m$$   and its mean distance from the earth is $$1.5 \times {10^{11}}m.$$   What is the diameter of the sun’s image on the paper ?

A. $$9.2 \times {10^{ - 4}}m$$  
B. $$6.5 \times {10^{ - 4}}m$$
C. $$6.5 \times {10^{ - 5}}m$$
D. $$12.4 \times {10^{ - 4}}m$$
Answer :   $$9.2 \times {10^{ - 4}}m$$
Solution :
The diameter of the sun, $$O = 1.39 \times {10^9}m$$    and its image is $$I.$$ As the distance of sun from lens $$u = 1.5 \times {10^{11}}m$$    and from paper is $$v = 0.1\,m.$$
Then by using relation
$$\eqalign{ & \frac{I}{O} = \frac{v}{u} \cr & \Rightarrow \frac{I}{{1.39 \times {{10}^9}}} = \frac{{0.1}}{{1.5 \times {{10}^{11}}}} \cr} $$
we get $$I = 9.2 \times {10^{ - 4}}m$$

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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