Answer to Question #153443 in Optics for hannah

Question

Explain how two thin prisms can be combined to produce without dispersion deviation of the mean light. obtain an expression for the resultant deviation

Answer 1

Answer

two thin prisms can be combined to produce without dispersion deviation of the mean light can be told as below theoritical aspects. In this combination, the deviation for the mean colour produced by one prism is annulled by the deviation produced for that colour by another prism is considered. However, after passing through the two prisms, there is some dispersion of light left thus kind of combination is used in direct vision spectroscope.

C is crown glass and F is flint glass prism. They are joined with their bases opposite the angles A₁and A₂ of these prisms are so chosen that the resultant deviation is zero and there is only dispersion which is called dispersion without deviation.

obtain an expression for the resultant deviation-

Suppose the refractive indices of crown and flint glass prisms for mean ray are μ and μ' deviation of mean ray by crown prism.

$\delta=(\mu-1) A_1$

Deviation of ray by flint prism can be expressed as below

$\delta'=(\mu'-1) A_2$

But resultant deviation is zero

So

$\delta=-\delta'$

$A_2=-\frac{(\mu-1)}{(\mu'-1)}A_1$

This negative sign shows that the refracting angles of both the prisms are in opposite directions.