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.

Answer

(i)`lambda_(0)=600nm,n=-1.5`(ii)i=sin^(-1)(0.75)=48.59^(@)`

Explanation

For given condition
`n_(1)=1.20+(10.8xx10^(4))/(lambda_(0)^(2))` and `n_(2)=1.45+(1.80xx10^(4))/(lambda_(0)^(2))`
for given condition `n_(1)=n_(2)`
`1.20+(10.8xx10^(4))/(lambda_(0)^(2))=1.45+(1.80xx10^(4))/(lambda_(0)^(2))`
`(9xx10^(4))/(lambda_(0)^(2))=0.25 rArr lambda_(0)^(2)=36xx10^(4)`
`n_(1)=1.20+(10.8xx10^(4))/(36xx10^(4))=1.5`
`n_(1)=n_(2)=1.5`
(ii) for `delta=delta_(m),r_(1)=r_(2)=(A)/(2)`
`n=(sin i)/(sin r_(1)) rArr n=(sin i)/(sin A//2)`
`sin i=1.5sin 30^(@)`
`i=sin^(-1)(0.75)`