Question

An equviconvex lens of crown glass and an equviconcave lens of flint glass make an achromatic system. The radius of curvature of convex lens is 0.54m. If the focal length of the combination for mean colour is 1.50mand the refractive indices for the crown glass are μR= 1.53 & μv= 1.55. Find the dispersive power of flint glass 

(a) 1/18 = .055 

(b) 2/18 

(c) 3/18 

(d) none 

Answer 1

Correct Option :- (a) 1/18 = .055 

Explanation :-

As for a lens 1/f =(μ-1) [(1/R₁)-(1/R₂)] 

R₁=R₂ =R = 54cm μ_y = (μ_v + μ_R)/2 = 1.54 (given) 

for convex lens 1/f_c =(1.54-1) [(1/54)-(1/-54) 

1/f_c =(1.54-1) [(1/54)+(1/54)] gives f_Crown = 50 cm (1) 

now as combination of two thin lenses in contact 1/f_c + 1/f_F =1/f 

1/50+1/f_F=1/150 gives f_lint = -75cm (2) 

As the system is achromatic ω_f /f_F + ω_c/f_c =0 

ω_c = (μ_v - μ_R) / μy-1 = 1.55-1.53/1.54-1 = 1/27 (3) 

Substituting the values of f_c , f_f & ωc in ωf /fF + ω_c/f_c =0 

ω_f = - ω_c (ff / fc) =-(1/27)(-75/50)=1/18=0.055