Figure shows a ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, show that (i) `r_(1) = r_(2) = A//2`, (ii) angle of minimum deviation, D or `D_(m) = 2i -A`.

Explanation

(i) From give figure, `A = r_(1) + r_(2)`
As ray QR is parallel to the base BC,
then `r_(1) = r_(2)`, and i = e
Therefore, `2r_(1) ` ( or `2r_(2)) = A`
`rArr r_(1) = r_(2) = A//2`
(ii) `D = x+y` `D = ( i - r_(1)) + ( e- r_(2))`
`D = ( i +e ) - ( r_(1) + r_(2))`
or `D = 2i -A`