Question

A concave lens of focal length 30 cm forms the image of an object of size 6 cm on the same side as the object at a distance of 10 cm from its optical centre. Determine the distance of the object from the lens.

Answer 1

Answer:

Explanation:

An object is placed 30 cm in front of convex lens of focal length 10 cm :

Given :  u₁ =−30 cm        f₁  =10 cm

From lens formula,    1/v₁-1/u₁ = 1/f₁

∴ 1/v₁-1/-30 = 1/10

⟹v=15 cm

Thus image is formed at a distance of 15 cm behind the lens.

Now a concave lens of focal length f₂   is placed in contact with convex lens. so the screen has to be shifted by 45 cm further away.

Now the new image distance   v₂  =15+45=60 cm

Let the focal length of combination of lens be F.

Using lens formula,    

1/v₂-1/u₂ = 1/F

∴  1/60 -1/-30 = 1/F    

⟹F=20 cm

Focal length of combination of lenses

1/F = 1/f₁ + 1/f₂      

∴    1/20 = 1/10 +1/f₂            

⟹f₂ =−20 cm    (minus sign comes as the focal length of concave lens is negative)