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 p_s = +26 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

Given,

Object distance, u = 26 cm, Focal length, f = 40 cm

(a) Radius of curvature, r = 2 x f = 2 x 40 = 80 cm

(b) let the image distance be v,

using the Lens Maker's formula,

1/f = 1/v + 1/u

(1/40) = (1/v) + (1/26)

Image distance, v = -74.28 cm

(c) Magnification, m = - v / u

m = -( - 74.28 / 26) = 2.857

(d) The image produced is virtual.

(e) The image is non inverted.

(f) The image is on the same side of the mirror.

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