Question

The refracting angle of a prism is $$A,$$ and refractive index of the material of the prism is $$\cot \left( {\frac{A}{2}} \right).$$   The angle of minimum deviation is

A. $${180^ \circ } - 3A$$
B. $${180^ \circ } - 2A$$  
C. $${90^ \circ } - A$$
D. $${180^ \circ } + 2A$$
Answer :   $${180^ \circ } - 2A$$
Solution :
$$\eqalign{ & {\text{As, we know that}}\,\,\mu = \frac{{\sin \left( {\frac{{A + {D_m}}}{2}} \right)}}{{\sin \frac{A}{2}}} \cr & \Rightarrow \cot \frac{A}{2} = \frac{{\sin \left( {\frac{{A + {D_m}}}{2}} \right)}}{{\sin \frac{A}{2}}} \cr & \Rightarrow \frac{{\cot \frac{A}{2}}}{{\sin \frac{A}{2}}} = \frac{{\sin \left( {\frac{{A + {D_m}}}{2}} \right)}}{{\sin \frac{A}{2}}} \cr & \Rightarrow \sin \left( {\frac{\pi }{2} - \frac{A}{2}} \right) = \sin \left( {\frac{{A + {D_m}}}{2}} \right) \cr & \Rightarrow \frac{\pi }{2} - \frac{A}{2} = \frac{A}{2} + \frac{{{D_m}}}{2} \cr & \Rightarrow {D_m} = \pi - 2A \cr & \therefore {D_m} = {180^ \circ } - 2A \cr} $$

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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