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Chapter 2: Problem 136

Find the focal length of a meniscus lens with \(R_{1}=20 \mathrm{cm}\) and \(R_{2}=15 \mathrm{cm} .\) Assume that the index of refraction of the lens is \(1.5 .\)

Short Answer

Expert verified
Therefore, the focal length of the meniscus lens is approximately \( 120 cm \).

Step by step solution

01

Identifying the given

Identify the given in the problem. Here we are given: \( R_1 = 20 cm, R_2 = 15 cm \) which are the radii of curvature of the lens' surfaces, and \( n = 1.5 \) which is the refractive index of the lens material.
02

Applying Lensmaker's formula

The lensmaker's formula for a thin lens is given as: \( \frac{1}{f} = (n - 1)( \frac{1}{R_1} - \frac{1}{R_2} )\), where \( f \) is the focal length, \( n \) is the index of refraction and \( R_1 \) and \( R_2 \) are the radii of curvature of the lens' surfaces. Now we just insert the given values into the formula.
03

Solving for focal length

After inserting the given values into lensmaker's formula: \( \frac{1}{f} = (1.5 - 1)( \frac{1}{20 cm} - \frac{1}{15 cm} )\), it simplifies to : \( \frac{1}{f} = 0.5(cm^{-1}) * (0.05 cm - 0.0667 cm)\). Further simplifying gives: \( \frac{1}{f} = -0.5 * (-0.0167 cm) = 0.00835 cm^{-1}\). The focal length will be the reciprocal of this result.

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Most popular questions from this chapter

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person's face is \(12.0 \mathrm{cm}\) away? Explicitly show how you follow the steps in the Problem-Solving Strategy: Spherical Mirrors.

Can an image be larger than the object even though its magnification is negative? Explain.

Two lenses of focal lengths of \(f_{1}\) and \(f_{2}\) are glued together with transparent material of negligible thickness. Show that the total power of the two lenses simply add.

What is meant by a negative magnification? What is meant by a magnification whose absolute value is less than one?

Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?
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