Question

The lens equation is 1f=1p+1q, where f is the focal length of the lens, p is the distance of the object from the lens, and q is the distance of the image from the lens. The formula to find q is

Answer 1

I will assume its as I suggested
Then rearranging:-

1/q = 1/f - 1/p

Answer 2

The required formula is
`q=(fp)/(p-f)`.

Explanation:

The given equation is

`(1)/(f)=(1)/(p)+(1)/(q)`

where,

1. f is the focal length of the lens.

2. p is the distance of the object from the lens.

3. q is the distance of the image from the lens.

We have to rearrange the formula for q.

Multiply both sides by fpq.

`(fpq)/(f)=fpq((1)/(p)+(1)/(q))`

`pq=(fpq)/(p)+(fpq)/(q)`

`pq=fq+fp`

Subtract fq from both the sides.

`pq-fq=fp`

Take out the common factor q.

`q(p-f)=fp`

Divide both the sides by (p-f)

`q=(fp)/(p-f)`

Therefore the required formula is
`q=(fp)/(p-f)`.