A prism of refractive index `n_(1)` & another prism of reactive index `n_(2)` are stuck together without a gap as shown in the figure.The angle of the prisms are as shown. `n_(1)&n_(2)`depend on`lambda`,the wavelength of light according to `n_(1)=1.20+(10.8xx10^(4))/(lambda^(2)) & n_(2)=1.45+(1.80xx10^(4))/(lambda^(2))` where `lambda` is in nm.

(i)Calculate the wavelength `lambda_(0)`for which rays incident at any angle on the interface`BC`pass through without bending at that interface.
(ii) for light of wavelength `lambda_(0)`,find the angle of incidencei on face`AC`such that the deviation produced by the combination of prism is minimum.

Explanation

(a) Light rays travel undaviated (in a straight line)if the refractive index of the medium does not change for any value of angle of incidence
`implies n_(1)=n_(2)`
`implies 1.2 + (10.8xx10^(4))/lambda_(0)^(2) = 1.45 + (1.8xx10^(4))/lambda_(0)^(2)`
`lambda_(0)=600nm`
`n_(0)= 1.2 + (10.8 xx10^(4))/lambda_(0)^(2)=1.5`
(b) If `n_(1)` and `n_(2)` are same the combination of prism will behave as a single prism of prism angle `60^@`.
`mu= sin((A+ delta_(m))/2)/sin(A//2)`
`implies "sin"(A+delta_(m))/2 = 3/4`
`implies (A+deltam)/2= 48.6^@ implies delta_(m)=37.2`
`r=30^@, sini=1.5 sin30^@=0.75`
`implies i=sin^(-1)0.75=48.6^@`