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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.

Text Solution

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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 occursfrom rarer `(mu_(1) = sqrt(2))` to denser medium `(mu_(2) = 1.514)`.
`:. -(mu_(1))/(u) + (mu_(1))/(v) = (mu_(2) - mu_(1))/(R )`
`(- 1.414)/(oo) + (1.514)/(v) = (1.514 - 1.414)/(0.4) = (1)/(4)`
`:. OE = v = 6.056 m`
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