Multiple Choice
When you look in your bathroom mirror in the morning, you see your reflection behind the mirror. If you are standing from the mirror, how far are you from the image of you?
33. Geometric Optics
Reflection of Light
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What is the distance, d, between the incoming and outgoing rays?
A
3.75 cm
B
26.7 cm
C
10.8 cm
D
11.8 cm
Verified step by step guidance1
Identify the geometry of the problem: The diagram shows a light ray reflecting off two surfaces, forming a rhombus-like shape. The angle of incidence and reflection is given as 68 degrees, and the vertical distance between the two parallel lines is 10 cm.
Understand the relationship between the angles and the sides: In a rhombus, opposite angles are equal, and adjacent angles are supplementary. The angle of incidence equals the angle of reflection, which is 68 degrees.
Use trigonometry to find the horizontal distance: The horizontal distance between the incoming and outgoing rays can be found using the tangent function. The tangent of the angle (68 degrees) is equal to the opposite side (vertical distance, 10 cm) divided by the adjacent side (horizontal distance, d).
Set up the equation using the tangent function: \( \tan(68^\circ) = \frac{10}{d} \).
Solve for d: Rearrange the equation to solve for d, which gives \( d = \frac{10}{\tan(68^\circ)} \). Calculate this value to find the distance between the incoming and outgoing rays.
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