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A convex mirror in an amusement park has a radius of curvature of 3. 00 m. A man stands in front of the mirror so that his image is half as tall as his actual height. At what distance must the man focus his eyes in order to see his image?.

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MrRoyal

The convex mirror in the park is an illustration of lens magnification

The man must focus his eyes at 4.50 meters to see his image

How to determine the object distance?

The given parameter is:

Radius of curvature, r = 3.00 m

The magnification (m) of the mirror is 1/2, because the image (v) is half as tall as the actual height (u).

So, we have:

m = u/v

So, we have:

u/v = 1/2

Make v the subject

v = 2u

The focal length is calculated as:

1/f = 1/u + 1/v

The focal length is calculated as:

f = r/2

f = 3/2

Substitute f = 3/2 in 1/f = 1/u + 1/v

2/3 = 1/u + 1/v

Substitute v = 2u in 2/3 = 1/u + 1/v

2/3 = 1/u + 1/2u

Take the LCM

2/3 = (2 + 1)/2u

This gives

2/3 = 3/2u

Take the inverse of both sides

3/2 = 2u/3

Cross multiply

2u = 3 * 3

4u = 9

Divide both sides by 4

u = 9/4

This gives

u = 2.25

Recall that:

v = 2u

So,we have:

v = 2 * 2.25

v = 4.50

Hence, the man must focus his eyes at 4.50 meters to see his image

Read more about magnification at:

https://brainly.com/question/2759705

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