Figure shows an irregular block of material of refractive indec `sqrt(2)`. A ray of light strikes the face AB as shown. After refraction, it is incident on a spherical surface CD of radius of curvature 0.4 m and enters a medium of refractive index 1.514 to meet PQ at E. Find the distance OE up to two places of decimal.

Explanation

As shown in Fig. refraction at `AB` is in going from rarer to denser medium.
:. `(mu_2)/(mu_1) = (sin i)/(sin r)`
`(sqrt(2))/(1) = (sin 45^@)/(sin r) = (1)/(sqrt(2) sin r)`
`sin r = (1)/(2), r = 30^@`
For refraction at surface `CD`, incident ray is parallel to `PQ`.
`:. u = oo, v = ?, R = 0.4 m`
Refraction occurs from rarer `(mu_1 - sqrt(2))` to denser medium `(mu_2 = 1.514)`.
`:. -(mu_1)/(u)+(mu_2)/(v) = (mu_2 - mu_1)/( R)`
`(-1.414)/(oo)+(1.514)/(v) = (1.514 - 1.414)/(0.4) = (1)/(4)`
`v = 4 xx 1.514 = 6.056 m`
`:. OE = v = 6.056 m`.
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