Question

A prism of angle 3${}^o$ is made of glass having refractive index 1.64. Two thin prisms made of glass having refractive index 1.48 are intended to be coupled with the former prism to yield a combination without a average deviation. Which of the following angles cannot correspond to the two prisms?

• A. 2${}^o$ and 2${}^o$
• B. 1.5${}^o$ and 2.5${}^o$
• C. 6${}^o$ and 2${}^o$
• D. 5.5${}^o$ and 3.5${}^o$

Answer 1

Answer: (D)

5.5${}^o$ and 3.5${}^o$

For the first prism :

Given - $A=3^o,\mu =1.64$

hence deviation by first prism

$\delta =A(\mu -1)=3(1.64-1)=1.92$

For the second prism :

Given - $\mu =1.48$

deviation by prism

${\delta }_2=A_2(\mu -1)=A_2(1.48-1)=0.48A_2$

For the third prism :

Given - $\mu =1.48$

deviation by prism

${\delta }_3=A_3(\mu -1)=A_3(1.48-1)=0.48A_3$

Net deviation by the combination of second and third prism ,

${\delta }^{\prime }={\delta }_2+{\delta }_3$

or ${\delta }^{\prime }=0.48A_2+0.48A_3$

As given , the average deviation is zero therefore the net deviation by second and third prism must be equal to the deviation by first prism .

$\delta ={\delta }^{\prime }$

or $1.92=0.48A_2+0.48A_3$

or $A_1+A_2=4$

Hence , the sum or difference (if placed in opposite manner) of angles of second and third prism must be $4$ , out of the given options $5.5,3.5$ doesn't satisfy this , hence this cannot correspond to two prisms .