Q. 74.4( 35 Votes )

Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20cm?

Answer :

Given Data:


Refractive index of glass, μ = 1.55


Focal length of the double-convex lens, f = 20 cm


Consider,


Radius of curvature of one face of the lens = R1


Radius of curvature of the other face of the lens = R2


Radius of curvature of the double-convex lens = R


Since it is mentioned that both faces are of the same radius,


R1 = R and R2 = -R


The value of R can be calculated as: t


… (1)


(Explanation: The above formula is generated by the ray diagram of the double convex lens. )


Substituting the given data in the equation (1), we get,




R = 0.55 × 2 × 20


R = 22 cm


Hence, the radius of curvature of the double-convex lens is 22 cm.


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