Question

when you hold a spherical concave mirror with a 48.2-cm radius of curvature in front of your face, you see an image of your face that is 61.8 cm in front of the mirror. what is the distance between the mirror and your face?

Answer 1

The distance between the mirror and your face is 39.5 cm

Using the mirror formula 2/r = 1/u + 1/v where r = radius of curvature = - 48.2 cm, u = distance between mirror and your face = object distance and v = distance between image and your face = - 61.8 cm. The distances are negative since the image is in front of the mirror and distances to the left of the mirror are negative.

So, making u subject of the formula, we have

2/r = 1/u + 1/v

1/u = 2/r - 1/v

1/u = (2v - r)/rv

u = rv/(2v - r)

Substituting the values of the variables into the equation, wse have

u = -48.2 cm × -61.8 cm/(2 × -61.8 cm - (-48.2 cm))

u = 2978.76 cm²/(-123.6 cm + 48.2 cm)

u = 2978.76 cm²/-75.4 cm

u = -39.51 cm

u ≅ -39.5 cm (The distance is negative since it is in front of the mirror)

So, the distance between the mirror and your face is 39.5 cm

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