Question

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 2.0 m behind the mirror, as shown in the figure(Figure 1) .

If you now place a pencil under the edge of the mirror nearer the wall, tilting it upward by 5.0 ? , how much higher on the wall (?y) is the spot?

?y=_________cm

Answer 1

y 1 =d tan theta =2.0 m tan 32 = 1.25 m

y d = t2.0 m tan( 32 +10)= 1.80 m

?y= y2-y= 1.80 m- 1.25 m= 0.55 m = 55 cm

Answer 2

The original spot will be 2m*sin(32) = 1.06m up the wall

Now the spot will be 2.*sin(37) = 1.20m

so ?y = 1.20 - 1.06 = 0.143m higher