Question

The light bulb in your room is not very bright. You want to use a concave mirror to direct its illumination into a tight, parallel beam of light for reading. The radius of curvature of the mirror is 30 centimeters. At what distance from the mirror should you place the light bulb to produce this parallel light beam

Answer 1

To produce a parallel beam of light for reading using a concave mirror, you should place the light bulb 30 cm from the mirror.

Step-by-step explanation:

To produce a parallel beam of light for reading, you can use a concave mirror. The radius of curvature of the mirror is given as 30 centimeters. To determine the distance at which you should place the light bulb, you can make use of the formula: 1/f = 1/di - 1/do, where f is the focal length of the mirror, di is the image distance, and do is the object distance.

In this case, we want parallel light beams, so di can be considered infinite. Plug in the known values: 1/30 = 1/infinity - 1/do. Since 1/infinity is considered zero, the equation simplifies to: 1/30 = -1/do. Solving for do, we find that the distance from the mirror should be -30 cm. However, since negative distances don't make sense in this context, we take the absolute value and conclude that the light bulb should be placed 30 cm from the mirror to produce the desired parallel light beam.

Answer 2

A point source is to be used with a concave mirror to produce a beam of parallel light. The source should be placed midway between the center of curvature and the mirror. To solve this question you have to draw a ray diagram. Apply the mirror equation to determine the image distance and finally make sure that the first two steps are consistent with each other.

I hope this helps, Regards.