Question

A concave mirror has as a radius of curvature of 0.4m.find the position and size if the image of an object 0.2m high placed 0.8 m in front of the mirror

Answer 1

Using the mirror formula we can get the image distance.

Let u be the object distance, v the image distance and f the focal length then :

1/f = 1/u + 1/v

Focal length is twice the radius of curvature thus :

f = 0.4 / 2 = 0.2m

Applying this to the formula.

1 / 0.2 - 1/0.8 = > 10/2 - 10/8 = 30/8

8/30 = 0.267

0.3 to 1 dp

To get the image height, we need to get the magnification :

Magnification = image distance / object distance

0.3 / 0.8 = 3/8

Image height = 0.2 m

Magnification = image height b/ object height

3/8 = h / 0.2

h = 3/8 × 0.2 = 0.075 m

Which is 0.07m to 2dp. -— height of image.

0.3m — image distance.

Answer 2

Answer:

1/f = 1/u + 1/v

Focal length is twice the radius of curvature thus :

f = 0.4 / 2 = 0.2m

Applying this to the formula.

1 / 0.2 - 1/0.8 = > 10/2 - 10/8 = 30/8

8/30 = 0.267

0.3 to 1 dp

To get the image height, we need to get the magnification :

Magnification = image distance / object distance

0.3 / 0.8 = 3/8

Image height = 0.2 m

Magnification = image height b/ object height

3/8 = h / 0.2

h = 3/8 × 0.2 = 0.075 m

Which is 0.07m to 2dp. -— height of image.

0.3m — image distance.