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Chapter 31: Problem 23

By holding a magnifying glass \(25 \mathrm{cm}\) from your desk lamp, you can focus an image of the lamp's bulb on a wall \(1.6 \mathrm{m}\) from the lamp. What's the focal length of your magnifying glass?

Short Answer

Expert verified
The magnifying glass has a focal length of approximately 29.6 cm.

Step by step solution

01

Convert all measurements into the same units

Firstly, ensure all measurements are in the same units. Here, it is given that the distance from the lamp to the magnifying glass is 25 cm. Convert cm to m by multiplying 25 with 0.01, which equals to 0.25 m. So, this gives 'u' = -0.25 m. The negative sign indicates that the object is on the opposite side of the light being refracted. The image distance 'v' is given as 1.6 m.
02

Substitute 'u' and 'v' into the lens equation

The lens equation is \(1 / f = 1 / v + 1 / u\). Substituting 'u' = -0.25 and 'v' = 1.6 into the lens formula, the equation becomes \(1 / f = 1 / 1.6 + 1 / (-0.25)\).
03

Solve the equation for 'f'

By solving the equation, \(1 / f = (1 / 1.6) - (1 / 0.25)\) becomes \(1 / f = 0.625 - 4\), which equals to -3.375. Since the focal length cannot be negative, 'f' is taken as the reciprocal of -3.375, which equals to approximately -0.296 m or -29.6 cm.
04

Interpret the result

The negative sign indicates that the focal length is on the same side as the object relative to the lens, which is typical in a magnifying glass. Therefore, the focal length of the magnifying glass is 29.6 cm.

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Most popular questions from this chapter

(a) Find the focal length of a concave mirror if an object placed \(38.4 \mathrm{cm}\) in front of the mirror has a real image \(55.7 \mathrm{cm}\) from the mirror. (b) Where and what type will the image be if the object is moved to a point \(16.0 \mathrm{cm}\) from the mirror?

How can you see a virtual image, when it's not "really there"?

A contact lens is in the shape of a convex meniscus (see Fig. 31.25 ). The inner surface is curved to fit the eye, with curvature radius \(7.80 \mathrm{mm}\). The lens is made from plastic with refractive index \(n=1.56 .\) If it has a \(44.4-\mathrm{cm}\) focal length, what's the curvature radius of its outer surface?

A double-convex lens with equal 28.5 -cm curvature radii is made from glass with refractive indices \(n_{\mathrm{red}}=1.512\) and \(n_{\text {violet }}=1.547 .\) If a point source of white light is located on the lens axis at \(75.0 \mathrm{cm}\) from the lens, over what distance will its visible image be smeared?

The cornea of the human eye has refractive index \(1.38,\) while the eye's lens has a graduated index in the range 1.38 to \(1.40 ;\) use 1.39 for this problem. For the aqueous humor between cornea and lens, \(n=1.34 .\) Find the angle through which light is deflected at the first surface of (a) the cornea and (b) the lens, if it's incident at \(20^{\circ}\) to the normal at each surface. Your result shows that the cornea is the dominant refractive element in the eye.
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