Two plane mirrors are facing each other. They are parallel, 5.00 cm apart, and 30.0 cm in length, as the drawing indicates. A laser beam is directed at the top mirror from the left edge of the bottom mirror. What is the smallest angle of incidence with respect to the top mirror, such that the laser beam hits each mirror only twice.

The minimum angle of incidence is, ∅ = 56° 18' 35'' to the normal

Explanation:

Given data,

The distance between the two plane mirror, d = 5 cm

The length of the plane mirror, L = 30 cm

According to the laws of reflection, the angle of incidence is equal to the angle of reflection.

If the laser beam touches each mirror only twice, then the base of the triangle formed is not less than L/2.

Let ∅ be the angle of incidence to the normal. The normal divides the triangle into two equal halves where base becomes L/4.

Therefore,

tan ∅ = opp / adj

= (L/4) / d

= (30/4) / 5

tan ∅ = 1.5

∅ = tan ⁻¹ (1.5)

= 56° 18' 35''

Hence, the minimum angle of incidence is, ∅ = 56° 18' 35'' to the normal.