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) The ray incident on BC passes undeflected through it
If `n_1=n_2` for wavelength `lambda_0`
`1.20+(10.8xx10^4)/(lambda_0^2)=1.45+(1.8xx10^4)/(lambda_0^2)`
`((10.8-1.8)xx10^4)/(lambda_0^2)=1.45-1.20`
`lambda_0^2=(9xx10^4)/(0.25)implieslambda_0=(3xx10^2)/(0.5)=600nm`
(b) For `lambda_0=600nm`, `n_1=n_2=1.2+(10.8xx10^4)/((600)^2)=1.5`
Now complete the prism, angle of prism, `A=60^@`

When angle of deviation is minimum, `r=A//2=30^@`
Refraction on AC: `1xxsini=muxxsinr`
`sini=1.5xxsin30^@=0.75`
`i=sin^-1(0.75)`