Mirror height to reflect bulb light onto right wall

[physicsismydaddy]

Need some help on a practice physics problem.

You need to place a mirror on the left wall, so that the reflected light from the bulb exactly fills the right wall.

ceiling
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3m | |
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4m
- the light bulb is 1m away from the left wall, it looks like it is centered.
a. what is the proper height of the mirror?
b. how far below the ceiling should the edge of the mirror be?
c. a 10cm tall screen to the right of the bulb from illuminating the right wall directly, what is the height of the screen's shadow on the right wall?

how I've approached the problem thus far: I started by stating that the angle that the top right corner makes with the mirror's top should be theta reflective and the other angle to the source from the mirror would be theta incidence due to the law of reflection. I'm lost as to where to go from here.

 

[ehild]

You need to place a mirror on the left wall, so that the reflected light from the bulb exactly fills the right wall.

how I've approached the problem thus far: I started by stating that the angle that the top right corner makes with the mirror's top should be theta reflective and the other angle to the source from the mirror would be theta incidence due to the law of reflection. I'm lost as to where to go from here.

And you know that theta reflective equals to theta incidence.
You can find the edges of the mirror easily by connecting the top (bottom) of the wall and the mirror image of the source by straight lines. See the figure attached.

ehild

 

[wais]

a. To find the proper height of the mirror, we can use the law of reflection which states that the angle of incidence (θi) is equal to the angle of reflection (θr). Since the light bulb is 1m away from the left wall and it appears to be centered, we can assume that the angle of incidence is 45 degrees (θi = 45 degrees). This means that the angle of reflection is also 45 degrees (θr = 45 degrees).

Now, we can use trigonometry to find the height of the mirror. We know that the distance from the left wall to the ceiling is 3m and the distance from the light bulb to the left wall is also 3m. Using the tangent function, we can set up the following equation:

tan 45 degrees = height of mirror / 3m

Solving for the height of the mirror, we get:

height of mirror = 3m * tan 45 degrees = 3m * 1 = 3m

So, the proper height of the mirror should be 3m.

b. To find how far below the ceiling the edge of the mirror should be, we can use the same trigonometric approach. Since the angle of reflection is 45 degrees, we can use the tangent function again to set up the following equation:

tan 45 degrees = distance from ceiling to edge of mirror / 3m

Solving for the distance from ceiling to edge of mirror, we get:

distance from ceiling to edge of mirror = 3m * tan 45 degrees = 3m * 1 = 3m

So, the edge of the mirror should be 3m below the ceiling.

c. To find the height of the screen's shadow on the right wall, we can use similar triangles. The height of the screen is 10cm and the distance from the light bulb to the right wall is 4m. This creates a triangle with a base of 4m and a height of 10cm.

We can use the ratio of the two sides of this triangle to find the height of the shadow. This ratio is equal to the ratio of the two sides of the larger triangle created by the light bulb, mirror, and right wall.

So, we can set up the following equation:

height of shadow / 4m = 10cm / 3