An object is placed a distance of 13.5 cm to the left of a thin converging lens

Question

An object is placed a distance of 13.5 cm to the left of a thin converging lens of focal length f = 6.60 cm, and a concave spherical mirror with radius of curvature +20.0 cm is placed a distance of 46.0 cm to the right of the lens (see figure below).

(a) What is the location of the final image formed by the lens–mirror combination as seen by an observer positioned to the left of the object?
cm to the left of the mirror

(b) What is the magnification of the final image as seen by an observer positioned to the left of the object? (Include the sign of the value in your answer.)

(c) Is the final image formed by the lens–mirror combination upright or inverted?

Explanation / Answer

the intermediate image from the length

1/13.5 +1/i = 1/6.6

1/I = 1/6.6 - 1/13.5 = 0.07744

I = 12.91 cm

The focal length of concave mirror = 10 cm

the object distance of the concave mirror = 46- 12.91 = 33.1 cm

1/33.1 +1/I = 1/10

1/I = 0.1-1/33.1

I= 14.33 cm

so the image is 14.33 cm to the left of the mirror.

M = -i1/o1 *(-i2/o2) = -12.91/13.5 * (-14.33/33.1) = 0.414

M >0 so the image is upright

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