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Figure shows an irregular block of mater...

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.

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The correct Answer is:
6.06 m
Applying Snell's law on face AB ,
`(1)"sin"45^(@)= (sqrt2)"sinr" therefore "sinr" = (1)/(2) "or" r = 30^(@)`
i.e., ray becomes parallel to AD inside the block .
Now applying , `(mu_(2))/(v) - (mu_(1))/(u) = (mu_(2) - mu_(1))/(R)` on face CD ,
`(1.514)/(OE) - (sqrt2)/(oo) = (1.514 - sqrt2)/(0.4)`
Solving this equation , we get `OE = 6.06` m
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