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

Use Snell's law
`n_1sini=n_2sinr`
Here, `n_1=1`,`n_2=sqrt2`,`i=45^circ`,`r=?`
`impliessinr=(1xxsin45^circ)/(sqrt2)=(1)/(2)impliesr=30circ`
The angle made by refracted ray at B with normal is `30^circ`. `:'`Angle made by the firs surface with refracted ray BC is `60^circ`.
Hence the refracted ray at B is parallel to horizontal arrow.
`:'` For refraction at spherical surface, `u=infty`
Now, `(n_2)/(v)-(n_1)/(u)=(n_2-n_1)/(R)`
`implies(1.514)/(v)=(1.514-1.414)/(0.4)` or `v=6.056`m
`:'` `OP=6.056m`