Final answer:
To strike the far end of the second mirror, the angle of incidence should be approximately 36.87°.
Step-by-step explanation:
To calculate the angle at which a beam of light should be incident at one end of a mirror so that it just strikes the far end of the other mirror, we can use the concept of reflection. When light reflects off a plane mirror, the angle of incidence is equal to the angle of reflection. In this case, since the mirrors are placed parallel to each other, the angle of incidence on one mirror will be the same as the angle of reflection on the other mirror.
Let's call the angle of incidence α. The angle of reflection on the first mirror will also be α. Now, we can consider the path of light from one mirror to the other. The light beam will reflect off the first mirror at an angle of α degrees, and it will travel a distance of 75 cm. Since the mirrors are 10 cm wide, the light beam will have to cover a total distance of 75 cm - 10 cm - 10 cm = 55 cm to reach the far end of the second mirror.
Using basic trigonometry, we can find the angle at which the light must be incident on the first mirror. We can use the ratio of the opposite side (55 cm) to the adjacent side (75 cm) to find the tangent of the angle. The equation is tan(α) = opposite/adjacent = 55 cm/75 cm.
To find α, we can use the inverse tangent function. α = tan-1(55 cm/75 cm) ≈ 36.87°.
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