A convex lens of focal length 20cm is placed 10cm away from a second convex lens of focal length 25 cm. What wil be the location of the image of an object at 30 cm in front of the first lens?

Explanation

Let the image from the first lens be formed at a distance y to the right of lens.
Refraction at the first lens:
Here, `u=-3cm, f=+20cm, v=+y`
From the lens equation, we get
`(1)/(v)-(1)/(u) =(1)/(f_(1))` or `(1)/(y)-(1)/(-30) =(1)/(20)or y=60cm`
Refraction at the second lens:
Here, `u=60-10=+50cm, f=+25cm`
Let the image be at a distance z to the right of lens2. Therefore, `v=+z. `
Substituting in the lens equation, we get
`(1)/(v)-(1)/(u) =(1)/(f_(2))` or`(1)/(z)=(1)/(25) +(1)/(50) or z=(50)/(3) cm`