# images of the plane mirror and the convex mirror

Suppose you walk with a speed of 1.20 m/s toward a plane mirror. What is the speed of your image relative to you, when your velocity is

(a) perpendicular to the mirror and

(b) at an angle of 45.0Â° with respect to the normal to the mirror?

Convex mirrors are being used to monitor the aisles in a store. The mirrors have a radius of curvature of 4 m.

(a) What is the image distance if a customer is 19 m in front of the mirror?

(b) If a customer is 1.7 m tall, how tall is the image?

https://brainmass.com/physics/mirrors/images-plane-mirror-convex-mirror-168979

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please see the attached file.

Suppose you walk with a speed of 1.20 m/s toward a plane mirror. What is the speed of your image relative to you, when your velocity is

(a) perpendicular to the mirror and

Suppose you start 2.4 meters away from the mirror. Then the distance between you and your image is 2*2.4 = 4.8 meters. After one second of walking, you will be (2.4-1.2) = 1.2 meters away from the mirror and your image will be 1.2 meters behind the mirror. The distance from you to your image is now 2.4 meters. So in one second, the distance between you and your image has changed by 4.8 - 2.4 = 2.4 meters. That is a speed of 2.4 meters/sec. So your image approaches you at the speed of 2.4 meters/sec.

(b) at an angle of 45.0Â° with respect to the normal to the mirror?

Assume initially you are at A, and your image is at A'

AO = A'O = ACsin45Â°.

The distance between you and your image is AA' = 2ACsin45Â°

After t seconds, you are at position B, and your image is at B'. then AB = 1.2t meters.

BO' = B'O' = BCsin45Â°

The distance between you and your image is BB' = 2BCsin45Â°.

Therefore, in t seconds, the distance between you and you image has changed by

AA' - BB' = 2 (AC - BC) sin45Â° = 2ABsin45Â°

d = AA' - BB' = 2*1.2tsin45Â°.

therefore, the speed of the image relative to you is

Convex mirrors are being used to monitor the aisles in a store. The mirrors have a radius of curvature of 4 m.

(a) What is the image distance if a customer is 19 m in front of the mirror?

The object (customer) so = 19 m. the radius R = -4 m for a convex mirror.

Using the mirror formula,

So the image is 2.235 m from the mirror.

(b) If a customer is 1.7 m tall, how tall is the image?

The magnification is

The image is 0.2 m tall. The negative sign indicates the image is inverted.

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