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 = +24 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 36 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. Spherical mirrors. Object O stands on the central axis of a spherical mirror. For this situation object distance is ps = +24 cm, the type of mirror is concave, and then the distance between the focal point and the mirror is 36 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

Given,

object distance = o = +24 cm ; focal length = 36 cm

a)The radius of curvature is related to focal length as:

R = 2f = 2 x 36 = 72 cm

Hence, R = +72 cm (since its a concave mirror so positive)

b)we know from lens eqn

1/f = 1/i + 1/o

i = o x f/(o + f)

i = 24 x 36/(24 + 36) = 14.4 cm

Hence, i = 14.4 cm

c)we know that magnification is given by:

M = -i/o = -14.4/24 = -0.6

Hence, M = 0.6

d)The image is real

e)It is inverted.

f)On the apposite side.

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