A crown glass prism of refracting angle `6^@` is to be used for deviation without dispersion with a flint glass of angle of pris`alpha` . Given: for crown glass `mu_r = 1.513 and mu_v = 1.523`, for flint glass `mu_r = 1.645 and mu_v = 1.665`. What should be the value of `alpha` ?

Explanation

The condition for deviation with out dispersion is
` ( mu_A - mu_R ) A = (mu_V - mu _R )A`
` therefore A.= ( ( 1.524 -1.514 )xx 8^0)/( (1.665 - 1.645 )) = ( 0.08^0)/(0.02 )= 4^0`
Mean refractive index for crown glass
`mu= ( 1.514 + 1.524)/( 2) = 1.519`
Mean refractive index for flint glass
`mu+ (1.645 + 1.665 ) /( 2) = 1.655`
` therefore ` The net deviation `( delta - delta .) = ( mu-1) A - ( mu.-1) A.`
`=0.159 xx 8^0 - 0.655 xx 4^0`
` = 1.53^@`