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Chapter 31: Problem 18

A virtual image is located \(40 \mathrm{cm}\) behind a concave mirror with focal length \(18 \mathrm{cm} .\) (a) Where is the object? (b) By how much is the image magnified?

Short Answer

Expert verified
The object is located 72cm in front of the mirror and the image is magnified by a factor of 5 / 9 (reduced).

Step by step solution

01

Utilize The Mirror Formula

Firstly, apply the mirror formula which is \(1/v + 1/u = 1/f\).
02

Substitute Given Values

Given that the virtual image is 40cm behind the mirror, so v = -40cm (The negative sign is due to the image being behind the mirror). The focal length (f) of the mirror is given as -18cm (It's negative for a concave mirror). Substitute these values into the mirror formula.
03

Calculate for u (Object Distance)

Upon substituting the values and solving for u (object distance), we get u = -72cm. The object is located 72cm in front of the mirror.
04

Utilize The Magnification Formula

Next, we use the magnification formula, magnification(m) = -v/u.
05

Substitute Values and Calculating Magnification

Substitute v as -40cm and u as -72cm into the formula, we get m = 40 / 72 = 5 / 9. This means the image is reduced, compared to the object.

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Most popular questions from this chapter

A candle and a screen are \(70 \mathrm{cm}\) apart. Find two points between candle and screen where you could put a convex lens with \(17-\mathrm{cm}\) focal length to give a sharp image of the candle on the screen.

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