Question

A 5 cm tall object is placed 68 cm from a convex mirror with a focal distance of -4 cm. The object is moved to 1cm from the same mirror. How would you calculate the distance to the image from the lens, the magnification, and the height of the image?

Answer 1

`d_i=-4/5cm`

`m=4/5cm`

`h_i=4cm`

Explanation:

We can begin by using the mirror equation to calculate the distance from the image to the mirror.

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

where `f` is the focal length of the mirror, `d_i` is the distance from the image from the mirror, and `d_o` is the distance from the object to the mirror.

We are given that `f=-4cm` and `d_o=1cm`, and we can use these values to solve for `d_i`:

`=>d_i=(1/f-1/d_o)^-1`

`=(-1/4-1)^-1`

`=-4/5cm`

Therefore, the image is formed behind the mirror and is said to be a virtual image.

We can now use the values for `d_i` and `d_o` to calculate the magnification of the mirror:

`m=-d_i/d_o`

`=-((-4/5))/1`

`=4/5`

Therefore, the image formed is reduced compared to the object size and upright.

Finally, we can use the values for `m` and `h_i` to find the height of the object:

`m=h_i/h_o`

`=>h_i=m*h_o`

`=4/5*5`

`=4cm`

`:. d_i=-4/5cm, m=4/5cm, h_i=4cm`