Question

An image formed by a diverging lens is only 1/4 as far from the lens as the object.Find the distance from the image to the lens if the focal length is 30 cm

Answer 1

In order to find the distance from the image to the lens, we can use the formula below:

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

Where f is the focal length (in m), do is the object distance and di is the image distance.

So, using f = 0.3 m and do = 4di, we have:

`\begin{gathered} (1)/(0.3)=(1)/(4d_i)+(1)/(d_i)\\ \\ (1)/(0.3)=(1+4)/(4d_i)\\ \\ (1)/(0.3)=(5)/(4d_i)\\ \\ 4d_i=5\cdot0.3\\ \\ 4d_i=1.5\\ \\ d_i=(1.5)/(4)\\ \\ d_i=0.375\text{ m} \end{gathered}`

Therefore the distance from the image to the lens is 37.5 cm.