Concave Mirror Problems

Question

The famous Chinese magician Foo Ling Yu performs a classic magic trick using a concave mirror with a focal length of 1.6 m. Foo uses the mirror to produce an image of a light bulb that is the same size as the light bulb itself and is at the same location. Explain, in complete sentences, how Foo accomplishes this magic trick. Be specific about the location of the light bulb.

Sometimes, when you sit by a lake in a forest, you can see perfect images of the hills and trees in the lake. Other times, when you are sitting beside the same lake, you cannot see any images in the water. Explain the difference between these two situations.

Answer 1

Question 1:

The formula for reflection from a concave mirror is:

 

1/f = 1/s + 1/s'

 

where f is he focal length (1.5 m), s is the distance of the object from the mirror, and s' is the distance of the image from the mirror.  Suppose we place the object at a distance of 3 meters from the mirror along the optical axis.  Where will the image be?

 

1/(1.5) = 1/3 + 1/s'

2/3 = 1/3 + 1/s'

2/3 - 1/3 = 1/s'

1/3 = 1/s'

3 = s'

 

The image will be the same distance from the mirror as the object; that is, it will be at the same location along the optical axis.  But will it be the same size? The formula for the magnification of a concave mirror is:

 

M = -s'/s

M = -3/3 = -1

 

The one means the image is the same size as the object.  The negative sign means it's inverted, or upside down.

 

Question 2:

When it comes to surfaces such as water, there are two types of reflection, specular and diffuse.  Specular reflection means the surface of the water is very still with no waves and acts just like a mirror, producing a perfect reflection of the hills and trees.  But if the wind picks up a little, it causes waves along the surface of the water so it is no longer flat and mirror like.  Instead light gets scattered in different directions and is not able to form a clear image of anything.  This is called diffuse reflection.