A spherical mirror is to be used to form an image 4.60 times the size of an obje

Question

A spherical mirror is to be used to form an image 4.60 times the size of an object on a screen located 4.00 m from the object.

(a) Is the mirror required concave or convex?

(b) What is the required radius of curvature of the mirror?

(c) Where should the mirror be positioned relative to the object?

_______________________________

I have done this problem multiple times. I will tell you the incorrect answers:

p, which is the distance from the object to the mirror is NOT 0.86, 1.11, or 1.66. If you get any of these answers, then it is wrong.

Many people assume that the 4.0 meters is the distance from the mirror to the image, but I believe this is an incorrect assumption. I assumed that it was q-p=4.0 meters, which was the method that gave me 1.11 (an incorrect answer for p).

If any expert has another way to try it, please let me know! Thanks in advance, even if you get it wrong!

Explanation / Answer

c)
Since the image has to be collected onto a screen it must be a real image.
A real image is always inverted, so magnification is negative

here the magnification is = - 4.60

then by using the formula

M = - di / do

4.60= 4.00 / do

do = 0.87 m

the mirror be positioned relative to the object at 0.87 m

b)

then by using mirror formula

1 / f = 1 / v + 1 / u

f = 1 / ( 1 / 4.00 + 1 / 0.87)

f = 0.715 m

the focal length of the mirror is 0.715m

the radius of curvature = 2 * 0.715 = 1.43m

a)

the mirror is concave mirror

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