Question

A person can see clearly objects only when they lie between $$50\,cm$$  and $$400\,cm$$  from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be

A. convex, + 2.25 diopter
B. concave, - 0.25 diopter  
C. concave - 0.2 diopter
D. convex, + 0.15 diopter
Answer :   concave, - 0.25 diopter
Solution :
Image of object at $$\infty $$ must lie within distance upto which person can view clearly.
Image distance, $$v = 400\,cm = 4\,m \Rightarrow u = \infty $$
Using lens equation, $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
$$\eqalign{ & \Rightarrow \frac{1}{{ - 4}} - \frac{1}{\infty } = \frac{1}{f} \cr & \Rightarrow f = - 4\,m \cr} $$
Now power of the required lens is,
$$P = \frac{1}{f} = \frac{1}{{ - 4}} = - 0.25D$$
Thus, the person require a concave lens of power $$ - 0.25D.$$

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.
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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
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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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