Chapter 34: Q47P (page 1040)

A double-convex lens is to be made of glass with an index of refraction of $1.5$ .One surface is to have twice the radius of curvature of the other and the focal length is to be $60 mm$ . What is the (a) smaller and (b) larger radius?

Short Answer

Expert verified

Smaller radius of the lens is $45 mm$
Larger radius of the lens is $90 mm$

Step by step solution

Listing the given quantities

Refractive index of lens, $n = 1.5$

Focal length, $f = 60.0 mm$

Radius of one surface is twice the other, i.e., $r_{2} = - 2 r_{1}$

Understanding the concepts of lens maker equation

By using the Lens maker’s formula, we can find the radius of both curvatures of the lens.

Formula:

Lens maker’s formula

$\frac{1}{f} = (n - 1) (\frac{1}{r_{1}} - \frac{1}{r_{2}}) . . . 34 - 10$

(a) Calculations of the smaller radius of the lens

Lens maker’s formula is given by equation,

$\frac{1}{f} = (n - 1) (\frac{1}{r_{1}} - \frac{1}{r_{2}})$

Since one surface has twice the radius of the other and since one surface is convex to the incoming light while the other is concave, we can write,

$r_{2} = - 2 r_{1}$

So, we can get,

$\frac{1}{f (n - 1)} = (\frac{1}{r_{1}} + \frac{1}{2 r_{1}}) = \frac{3}{2 r_{1}} r_{1} = \frac{3}{2} f (n - 1) = 1.5 (60.0) (1.5 - 1) = 45 mm$

Smaller radius of the lens is $45 mm$ .

(b) Calculations of the larger radius of the lens

As per the condition given in the problem, r²will be double of r₁

So, r₂ = 90 mm

Larger radius of the lens is 90 mm

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A double-convex lens is to be made of glass with an index of refraction of $1.5$ .One surface is to have twice the radius of curvature of the other and the focal length is to be $60 mm$ . What is the (a) smaller and (b) larger radius?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of lens maker equation

(a) Calculations of the smaller radius of the lens

(b) Calculations of the larger radius of the lens

One App. One Place for Learning.

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A double-convex lens is to be made of glass with an index of refraction of 1.5.One surface is to have twice the radius of curvature of the other and the focal length is to be 60mm. What is the (a) smaller and (b) larger radius?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of lens maker equation

(a) Calculations of the smaller radius of the lens

(b) Calculations of the larger radius of the lens

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Electricity and Magnetism

Magnetism and Electromagnetic Induction

Circular Motion and Gravitation

Conservation of Energy and Momentum

Rotational Dynamics

Study anywhere. Anytime. Across all devices.

A double-convex lens is to be made of glass with an index of refraction of $1.5$ .One surface is to have twice the radius of curvature of the other and the focal length is to be $60 mm$ . What is the (a) smaller and (b) larger radius?