Question

A thin prism having refracting angle $${10^ \circ }$$ is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be

A. $${4^ \circ }$$
B. $${6^ \circ }$$  
C. $${8^ \circ }$$
D. $${10^ \circ }$$
Answer :   $${6^ \circ }$$
Solution :
For dispersion without deviation, net deviation produced by the combination of prisms must be zero.
Let, prism angle of the first and second prisms are $${A_1}$$ and $${A_2}$$ respectively. Similarly, their refractive indices are $${\mu _1}$$ and $${\mu _2}.$$
Condition for dispersion without deviation is
$$\eqalign{ & {\delta _1} - {\delta _2} = 0 \cr & \Rightarrow \left( {{\mu _1} - 1} \right){A_1} - \left( {{\mu _2} - 1} \right){A_2} = 0 \cr & \Rightarrow {A_2} = \left( {\frac{{{\mu _1} - 1}}{{{\mu _2} - 1}}} \right) \cr & {A_1} = \left( {\frac{{1.42 - 1}}{{1.7 - 1}}} \right)\left( {{{10}^ \circ }} \right) \cr & \Rightarrow {A_2} = {6^ \circ } \cr} $$

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

Practice More Releted MCQ Question on
Ray Optics


Practice More MCQ Question on Physics Section