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Chapter 34: Q41P (page 1040)

A lens is made of glass having an index of refraction of 1.5. One side of the lens is flat, and the other is convex with a radius of curvature of 20 cm(a) Find the focal length of the lens. (b) If an object is placed 40 cmin front of the lens, where is the image?

Short Answer

Expert verified
  1. The focal length of the lens is +40cm.
  2. If an object is placed 40 cm in front of the lens, then the image will be at ∞.

Step by step solution

01

Listing the given quantities

n=1.5r1=∞r2=-20cmp=40cm

02

Understanding the concepts of lens maker equation

Using lens maker’s equation, we can find the focal length for the given lens. We can find the image distance by using the equation for the thin lens.

Formula:

1f=(n-1)(1r1-1r2)1f=1i+1p

03

Calculations of the focal length of the lens

(a) The lens maker’s equation is given by

1f=(n-1)(1r1-1r2)1f=(1.5-1)(1∞-1-20)1f=0.5×0.05f=10.025

=+40cm

04

Calculations of the image distance 

(b)

We have, for thin lens,

1f=1i+1p

Rearranging the terms,

i=11f-1p=1140-140=10=∞

If an object is placed 40 cm in front of the lens, then the image will be at∞.

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Most popular questions from this chapter

You look down at a coin that lies at the bottom of a pool of liquid of depthand index of refraction(Fig. 34-57). Because you view with two eyes, which intercept different rays of light from the coin, you perceive the coin to bewhere extensions of the intercepted rays cross, at depthdainstead of d. Assuming that the intercepted rays in Fig. 34-57 are close to a vertical axis through the coin, show that da=dn.


You produce an image of the Sun on a screen, using a thin lens whose focal length is 20cm. What is the diameter of the image? (See Appendix C for needed data on the Sun.)

A small cup of green tea is positioned on the central axis of a spherical mirror. The lateral magnification of the cup is +0.250, and the distance between the mirror and its focal point is 2.00cm. (a) What is the distance between the mirror and the image it produces? (b) Is the focal length positive or negative? (c) Is the image real or virtual?

In Fig. 34-52, an object is placed in front of a converging lens at a distance equal to twice the focal length f1of the lens. On the other side of the lens is a concave mirror of focal lengthf2separated from the lens by a distance 2(f1+f2). Light from the object passes rightward through the lens, reflects from the mirror, passes leftward through the lens, and forms a final image of the object. What are (a) the distance between the lens and that final image and (b) the overall lateral magnification M of the object? Is the image (c) real or virtual (if it is virtual, it requires someone looking through the lens toward the mirror), (d) to the left or right of the lens, and (e) inverted or non-inverted relative to the object?

A millipede sits 1.0min front of the nearest part of the surface of a shiny sphere of diameter 0.70m(a) How far from the surface does the millipede’s image appear? (b) If the millipede’s height is 2.0mm, what is the image height? (c) Is the image inverted?
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