Question

Two point white dots are $$1\,mm$$  apart on a black paper. They are viewed by eye of pupil diameter $$3\,mm.$$  Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = $$500\,nm$$  ]

A. $$1\,m$$
B. $$5\,m$$  
C. $$3\,m$$
D. $$6\,m$$
Answer :   $$5\,m$$
Solution :
$$\eqalign{ & \frac{y}{D} \geqslant 1.22\frac{\lambda }{d} \cr & \Rightarrow \,\,D \leqslant \frac{{yd}}{{\left( {1.22} \right)\lambda }} \cr & = \frac{{{{10}^{ - 3}} \times 3 \times {{10}^{ - 3}}}}{{\left( {1.22} \right) \times 5 \times {{10}^{ - 7}}}} \cr & = \frac{{30}}{{6.1}} \cr & \approx 5\,m \cr & \therefore \,\,{D_{\max }} = 5\,m \cr} $$

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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