A butterfly at eye level is 22 cm in front of an plane mirror. You are behind the butterfly, 46 cm from the mirror. What is the distance between your eye and the image of the butterfly in the mirror?

No glass is perfectly transparent. Mainly because of reflections, about 90% of light passes through an average sheet of clear windowpane. The 10% loss is not noticed through a single sheet, but through several sheets it is apparent. How much light is transmitted by two sheets?

The distance is the distance between the butterfly and the mirror plus the distance between you and the mirror. So, it would be

D(total) = D(object) + D(eye)
Basic math.

To find the distance between your eye and the image of the butterfly in the mirror, we can use the mirror equation:

1/f = 1/d_o + 1/d_i

where f is the focal length of the mirror, d_o is the object distance, and d_i is the image distance.

Since the mirror is plane, the focal length is infinite (f = ∞). Therefore, the mirror equation simplifies to:

1/d_o + 1/d_i = 0

Substituting the given values, we have:

1/46 + 1/d_i = 0

To find d_i, we need to solve for it. Rearranging the equation, we get:

1/d_i = -1/46

Taking the reciprocal of both sides, we have:

d_i = -46

Since the distance should be positive, we ignore the negative sign. Thus, the distance between your eye and the image of the butterfly in the mirror is 46 cm.