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Chapter 31: Problem 25

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 focal length of the magnifying glass is approximately \(20.48 cm\).

Step by step solution

01

Convert units

The image distance (from the lamp to the wall) needs to be converted to centimeters to correspond with the unit of the object distance. Thus, \(1.6 m = 160 cm\).
02

Apply the lens formula

The lens formula states that \(1/f = 1/v - 1/u\). We have \(u = -25 cm\) and \(v = 160 cm\). Apply these values to the formula. Note that the 'object distance' is negative due to the convention that distances measured in the same direction as the light are positive.
03

Solve for f (focal length)

Now, solve the equation for f, which gives \(f = \frac{1}{\frac{1}{160}+\frac{1}{25}} cm\).

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Most popular questions from this chapter

Generalize the derivation of the lensmaker's formula (Equation 31.7) to show that a lens of refractive index \(n_{\text {lens }}\) in an external medium with index \(n_{\mathrm{ext}}\) has focal length given by $$\frac{1}{f}=\left(\frac{n_{\text {lens }}}{n_{\text {ext }}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$$

A double-convex lens with equal 38 -cm curvature radii is made from glass with refractive indices \(n_{\mathrm{red}}=1.51\) and \(n_{\text {violet }}=1.54\) If a point source of white light is on the lens axis \(95 \mathrm{cm}\) from the lens, over what range will its visible image be smeared?

LCD projectors commonly used for computer and video projection create an image on a small LCD display (see Application on page 345 ). The display is mounted before a lens and illuminated from behind. In a projector using a \(7.50-\mathrm{cm}\) -focal-length convex lens, where should the LCD display be located so the projected image is focused on a screen \(6.30 \mathrm{m}\) from the lens?

A 300 -power compound microscope has a 4.5 -mm-focal-length objective lens. If the distance from objective to eyepiece is \(10 \mathrm{cm},\) what should be the focal length of the eyepiece?

A particular eye has a focal length of \(2.0 \mathrm{cm}\) instead of the 2.2 \(\mathrm{cm}\) that would put a sharply focused image on the retina. (a) Is this eye nearsighted or farsighted? (b) What corrective lens is needed?
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