Question

Reflection of light?

1.) Sunlight enters a room at an angle of 32° above the horizontal and reflects from a small mirror lying flat on the floor.The reflected light forms a spot on a wall that is a distance d = 3.8m behind the mirror. Given that the mirror is horizontal (i.e. θ =0°), what is the height y of the spot on the wall (in centimeters)?

2.) If you now place a pencil under the edge of the mirror nearer the wall, tilting it upward by θ = 5° , how much higher on the wall Δy is the spot (in centimeters)?

Answer 1

(1) `y = 2.37` m `= 237` cm

(2) `\Delta y = 1.05` m `= 105` cm

Explanation:

Since the mirror is horizontal and the sun light is entering as parallel rays, the rays will reflect off the mirror with an angle equal to the angle of incidence.

We are given the horizontal distance from the point of reflection to the wall. So we can use some basic trigonometry to compute the height on the wall that the light will hit.

`tan\theta = (y)/(d)`

We have `\theta = 32^o` and `d = 3.8` m.

`y = d tan(\theta)`

`y = (3.8) tan(32^o) = 2.37` m

For the case where the mirror is tilted, the incident angle is now increased as well as the reflected angle. So the additional `5^o` is actually doubled in its effect on the reflection. So the reflected angle will be `10^o` greater than it was with the horizontal mirror.

`y = d tan(\theta`

`y = (3.8) tan(42^o)= 3.42` m

The difference in height is:

`\Delta y = 3.42 - 2.37 = 1.05` m