Please inlude ALL mathematical & conceptual steps soI can understand. Thanks. A

Question

Please inlude ALL mathematical & conceptual steps soI can understand. Thanks.
A convex mirror is on the exterior of the passenger side ofmany trucks. Assume the focal length of such a mirror is -46.0cm.

(a) What will be the location and height of the imageof a car that is 2.2 m tall and 100 m behind the mirror?
location
cm
height
cm
(b) What will be the location and height of the image of a car thatis 1.1 m tall and 10.0 m in front of the mirror?
location
cm
height
cm

Please inlude ALL mathematical & conceptual steps soI can understand. Thanks.
A convex mirror is on the exterior of the passenger side ofmany trucks. Assume the focal length of such a mirror is -46.0cm.

Explanation / Answer

Given, f = -0.46; u = 100 m; h1 = 2.2 m           1/v +1/u = 1/f becomes,           1/v =-1/0.46 - 1/100 = -100.46/46       Image distance, v = -46/100.46 = -0.458m           Applying h2/h1 = v/u             Heightof the image,                           h2 = h1.v/u = 2.2x0.458/100 = 0.010 m (b) Proceding as above, with u = 10 m; h1 = 1.1 m       1/v + 1/u = 1/f becomes,           1/v =-1/0.46 - 1/10 = -10.46/4.6       Image distance, v = -4.6/10.46 = -0.440m           Applying h2/h1 = v/u             Heightof the image,                           h2 = h1.v/u = 1.1x0.440/10                               = 0.0484 m

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