The radius of curvature of a mirror is 40 cm. A diamond ring is placed in front

Question

The radius of curvature of a mirror is 40 cm. A diamond ring is placed in front of this mirror. The image is four times the size of the ring. Is the mirror concave or convex, or is either type possible? How many places are there in front of a concave mirror where the ring can be placed and produce an image four times the size of the object? What are the possible values for the magnification of the image of the ring? (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.) (3 answers) Find the possible object distances of the ring. (Enter your answers from smallest to largest starting with the first answer blank. Enter NONE in any remaining answer blanks.)

Explanation / Answer

Convex mirror cannot form an enlarged image. So, the mirror is concave.

There are two places before a concave mirror where an image four times the size of the object can be created. One for object distance (u) within the focal length (f) and other for object distance between f anf 2f.

Magnification can achieve all values in case of concave mirror.

Focal length, f = 40/2 = 20 cm

Magnification, m = -v/u

Mirror formula:

1/v - 1/u = 1/f

Multiplying both sides by u, we get,

-1/m - 1 = u/f

=> u = -f(1 + 1/m)

Now, m = 4, -4

So,

u1 = -20(1 + 1/4) = -25 cm

u2 = -20[1 + 1/(-4)] = -15 cm

So, the image is four times larger than the object for object distances 15 cm and 25 cm from the concave mirror.

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