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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 鈭�.

Step by step solution

01

Listing the given quantities

n=1.5r1=鈭�r2=-20cmp=40cm

02

Understanding the concepts of lens maker equation

Using lens maker鈥檚 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鈥檚 equation is given by

1f=(n-1)(1r1-1r2)1f=(1.5-1)(1鈭�-1-20)1f=0.5脳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=鈭�

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

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Most popular questions from this chapter

A moth at about eye level is10鈥�cmin front of a plane mirror; a man is behind the moth,30鈥�cmfrom the mirror. What is the distance between man鈥檚 eyes and the apparent position of the moth鈥檚 image in the mirror?

A narrow beam of parallel light rays is incident on a glass sphere from the left, directed toward the center of the sphere. (The sphere is a lens but certainly not a thin lens.) Approximate the angle of incidence of the rays as 0掳, and assume that the index of refraction of the glass is n<2.0(a) In terms of n and the sphere radius r, what is the distance between the image produced by the sphere and the right side of the sphere? (b) Is the image to the left or right of that side? (Hint: Apply Eq. 34-8 to locate the image that is produced by refraction at the left side of the sphere; then use that image as the object for refraction at the right side of the sphere to locate the final image. In the second refraction, is the object distance positive or negative?)

17 through 29 22 23, 29 More mirrors. Object Ostands on the central axis of a spherical or plane mirror. For this situation, each problem in Table 34-4 refers to (a) the type of mirror, (b) the focal distance f, (c) the radius of curvature r, (d) the object distance p, (e) the image distance i, and (f) the lateral magnification m. (All distances are in centimeters.) It also refers to whether (g) the image is real localid="1662999140986" (R)or virtual (V), (h) inverted (I)or non-inverted from (NI)from O, and (i) on the same side of the mirror as the object Oor the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.

An object is 30.0cmfrom a spherical mirror, along the mirror鈥檚 central axis. The mirror produces an inverted image with a lateral magnification of absolute value 0.500. What is the focal length of the mirror?

32 through 38 37, 38 33, 35 Spherical refracting surfaces. An object Ostandson the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refractionn1where the objectis located, (a) the index of refraction n2on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature rof the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R)or virtual (V)and (f) on the same side of the surface asthe object Oor on the opposite side.
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