Question

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?

Answer 1

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`