How far from a concave mirror of radius 0.25m must an object be place for a real

Question

How far from a concave mirror of radius 0.25m must an object be place for a real image to be formed 1m from the mirror?  What is the magnification of that image?
4.A dentist uses a mirror that will produce an upright image with a lateral magnification of +3 when placed 2cm from a tooth.  What kind of mirror is it (concave or convex) and what is its radius of curvature?
5.The lateral magnification of a image in a convex mirror is 0.6 when the object is 2m from the mirror.  What is the focal length of the mirror?
6. A light beam traveling in air strikes a flat surface of an unknown material.  The angle of incidence is measured to be 40degrees and the angle of refraction is measured to be 20degrees.   a)What is the index of refraction of the material? b)What is the speed of light in that material?

How far from a concave mirror of radius 0.25m must an object be place for a real image to be formed 1m from the mirror?  What is the magnification of that image?
4.A dentist uses a mirror that will produce an upright image with a lateral magnification of +3 when placed 2cm from a tooth.  What kind of mirror is it (concave or convex) and what is its radius of curvature?
5.The lateral magnification of a image in a convex mirror is 0.6 when the object is 2m from the mirror.  What is the focal length of the mirror?
6. A light beam traveling in air strikes a flat surface of an unknown material.  The angle of incidence is measured to be 40degrees and the angle of refraction is measured to be 20degrees.   a)What is the index of refraction of the material? b)What is the speed of light in that material?

Explanation / Answer

f = R/2 = 0.25 / 2 = 0.125 m

1/u + 1/v = 1/f

1/0.125 = 1/u + 1/1

1/u = 7

u = 1/7m

magnification = 7

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4) the mirror must be concave. a convex mirror always produces a diminished virtual image

mirror eqn 1/s + 1/s' = 1/f = 2/r

r = 2 s s' / s' + s

lateral magnification of mirror m = -s' / s

r = -2 m s / 1 - m

= (-2 * 3 * 2) / (1 - 3)

= 6 cm

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