Q.

Plane wave fronts are incident on a glass slab which has refractive index as a function of distance z, according to the relation  μ=μ0 (1-z2/z02), where μ0 is the refractive index along the axis and z0 is a constant. This glass slab can act as lens of focal length f. By using the concept of optical path length calculate the focal length of the slab. Consider t to be very small as compared to f.

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a

z02/(0t)

b

z02/(μ0t)

c

μ0z02/(2t)

d

None

answer is A.

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Detailed Solution

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On comparing optical path we get

tμ0(1Z2Z0)+Z2+F2=tμ0+F

Z2+F2=μ0tZ2Z02+F      Z2+F2=μ02t2(Z2Z02)2+F2+2μ0tZ2Z02F

Since t is very small

Z2=2μ0tZ2Z02FF=Z02/(2μ0t)

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