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A quarter cylinder of radius R and refra...


A quarter cylinder of radius R and refractive index 1.5 is placed on a table.A point object P is kept at a distance of mR from it. Find the value of m for whicha ray from P will emerge parallel to the table as shown in the figure.

Text Solution

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The correct Answer is:
`4//3`
Applying `(mu_(2))/(v) - (mu_(1))/(u) = (mu_(2) - mu_(1))/(R)`
First on plane surface
`(1.5)/(Al_(1)) - (1)/(-mR) = (1.5-1)/(oo) = 0`
`therefore Al_(1) = -(1.5"mR")`
Then on curved surface
`(1)/(oo) - (1.5)/(-(1.5 mR + R)) = (1 - 1.5)/(-R)`
[`v = oo` because final image is at infinity]
`implies (1.5)/((1.5 m +1) R) = (0.5)/(R)`
`implies 3 = 1.5 m + 1 implies (3)/(2) m = 2 implies m = (4)/(3)`
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