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An object when placed in front of a plan...

An object when placed in front of a plano-convex lens forms a real image at a distance of 10 m behind the lens. The image that is formed is one-fourth of that of the size of the object. The wavelength of light that is inside the lens is `(3)/(4)` times the wavelength in free space. What is the radius of the curved surface of the lens in m?

Text Solution

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The correct Answer is:
`02.67`
`mu=(lambda_("vavum"))/(lambda_("med"))=(4)/(3)`
Given, `v= + 10m, m=(-1)/(4) =(v)/(u)`
`:.u=(v)/(m) = -40 m`
Using lens formula,
`(1)/(f) =(1)/(v) -(1)/(u) =(1)/(10) - (-(1)/(40))`
`:. (1)/(f) = (5)/(40) rArr f=8m`
For plano-convex lens,
`(1)/(f) =(mu-1) ((1)/(R ))`
`:.` Radius of curvature
`R= f(mu-1) =8 ((4)/(3)-1)`
`=2.67m`
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