Question

When a monochromatic light ray is incident on a medium of refracive index`mu`with angle of incidence `theta_(1)`,the angle of refraction is `theta_(r).`if `theta_(i)` is changed slightly by`Deltatheta_(i)`,then the corresponding change in `theta_(r)`will be-
A. `Delta Theta_(i)`
B. `muDeltatheta_(i)`
C. `(1)/(mu).cos theta_(1)/(cos theta_(r)).Delta theta_(i)`
D. `mu.sin theta_(1)/(sin theta_(r)).Delta theta_(i)`

Answer 1

Correct Answer - C
`mu=(sintheta_(i))/(sintheta_(r))`
`sintheta_(r)=(1)/(mu)sintheta_(i)`
Differentiate the equation with respect to`theta_(i)`
`costheta_(r)""(d theta_(r))/(d theta_(i))=(1)/(mu) costheta_(i)`
`d theta_(r)=(1)/(mu)(costheta_(i))/(costheta_(r))d theta_(r)`
`Delta theta_(r)=(1)/(mu)(costheta_(i))/(costheta_(r))d theta_(r)Delta theta_(i)`