A student notices that the image produced from a large skyscraper (h = 138 m) is

Question

A student notices that the image produced from a large skyscraper (h = 138 m) is inverted and the magnitude of the height is |h_i| = 1.01 m tall. The image is located d = 122 cm in front of the mirror. Write an expression mirror and the skyscraper, d_s select from the variable below to write your expression. Note all variables may not be required. Alpha, beta, theta, a, b, d, g, h, h_i, j, k, m,P, S, t Numerically, what is the distance in meters? A numeric value is expected and not an expression. Numerically, what is the focal point of the mirror, f, in cm? A numeric value is expected and not an expression.

Explanation / Answer

Here,

height of objct , h = 138 m
height of image , hi = 1.01 m

image distance, di = 122 cm = 1.22 m

part a) for the object distance ds

using d/ds = hi/h

ds = d * h/(hi)

the expression of the distance between the mirror and skyscrapper is d * h/(hi)

b)

numerically ,

ds = 1.22 * (138/1.01)

ds = 166.7 m

the distance between mirror and skyscapper is 166.7 m

c)

Using lens formula

1/f = 1/ds + 1/d

1/f = 1/166.7 + 1/1.22

f = 1.211 m

f = 121.1 cm

the focal point of mirror is 121.1 cm away

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