Question

An object 20cm high is placed 45cm from the lens of focal length 15cm? calculate the image distance and the size of the image and the nature of the image? If a concvex lens and a concave lens is used.

Answer 1

Image distance `d_i = 22.5 " cm"`

The image size is `h_i = -10 " cm"`, meaning that the image is inverted.

Explanation:

Given:
`h_o = 20 " cm"`

`d_o = 45 " cm"`

`f = 15 " cm"`

To calculate image distance, use the thin lens equation:

`(1/d_o) + (1/d_i) = 1/f`

`(1/45) + (1/d_i) = 1/15`

`1/(d_i) = 2/45`

`d_i = 22.5 " cm"`

To calculate image size, use the magnification equation:

`m = frac{h_i}{h_o} = frac{-d_i}{d_o}`

#frac{h_i}{20} = frac{-22.5}{45}

`h_i = (20)*(-1/2)`

`h_i = -10 " cm"`

If a convex lens is used, I think the image would be real. However, if a concave lens were used, I think the image would be virtual because it is a diverging lens.