Spherical mirrors. Object O stands on the central axis of a spherical mirror. Fo

Question

Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +22 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 40 cm (without proper sign). Find (a) the radius of curvature r (including sign), (b) the image distance i, and (c) the lateral magnification m. Also, determine whether the image is (d) real or virtual, (e) inverted from object O or noninverted, and (f) on the same side of the mirror as O or on the opposite side.

Explanation / Answer

Part A)

A concave mirror has a positive focal length and radius of curvature

R = 2f = 2(40)

R = 80 cm

Part B)

Apply 1/f = 1/p + 1/q

1/40 = 1/22 + 1/q

q = -48.9 cm

Part C)

M = -q/p

M = -(-48.9)/(22)

M = 2.22

Part D)

Since q is negative, the image is virtual

Part E)

Since M is positive, the image is not inverted

Part F)

Since the image is virtual, it is on the opposide side of the mirror as the object.

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