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 = R_{1}

Radius of curvature of the other face of the lens = R_{2}

Radius of curvature of the double-convex lens = *R*

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

⇒ R_{1} = R and R_{2} = -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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