You have a converging mirror with a focal length of 24 cm. When you place an obj

Question

You have a converging mirror with a focal length of 24 cm. When you place an object in front of the mirror, you observe that the mirror creates an image of the object that is 5 times larger than the object. What is the object distance?

(a) It turns out that there are two possible solutions. The smaller of these solutions is ... do = cm

(b) The larger of these solutions is ... do = cm

(c) Starting from either one of these locations, if you then move the object a little bit toward the focal point, the image will ... (select all that apply). move closer to the mirror move farther from the mirror stay the same distance from the mirror get smaller in size get larger in size stay the same size we can't choose any of the above - it actually depends which of the two object distances we start from

Explanation / Answer

given

f = 24 cm

let u and v are object and image distances.

a) if the image is virtual, m = +5

we know, m = -v/u

5 = -v/u

==> v = -5*u

now use, 1/u + 1/v = 1/f

1/u + 1/(-5*u) = 1/f

(1/u)*(1 - 1/5) = 1/f

(1/u)*(4/5) = 1/f

u = 4*f/5

= 4*24/5

= 19.2 cm <<<<<<<<<------------------Answer

b) if the image is real, m = -5

we know, m = -v/u

-5 = -v/u

==> v = 5*u

now use, 1/u + 1/v = 1/f

1/u + 1/(5*u) = 1/f

(1/u)*(1 + 1/5) = 1/f

(1/u)*(6/5) = 1/f

u = 6*f/5

= 6*24/5

= 28.8 cm <<<<<<<<<<--------------------Answer

c) move farther from the mirror

get larger in size

Because, as u approches f, v approches infinity.

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