Question

On placing a concave lens in the path of convergent rays, they focus on the axis in the back, 20 cm from the lens.
In the absence of a lens, where do the rays focus? The focal length of the lens is 30 cm.

Hint:

Concave lenses always produce {virtual, upright, and diminished} images, and they have a {negative focal length}.

Answer 1

The lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Given \( f = -30 \) cm (since it's a concave lens, the focal length is negative), and the image distance \( v = -20 \) cm (since the image is formed on the same side as the object in a concave lens), we can substitute these values into the lens formula to find the object distance \( u \).
Using the lens formula: \[ \frac{1}{-30} = \frac{1}{-20} - \frac{1}{u} \] Solving for \( u \): \[ \frac{1}{u} = \frac{1}{-20} - \frac{1}{-30} = -\frac{1}{60} \] Thus, the object distance is \( u = -60 \, \text{cm} \).
So, the answers are:
(i) The object distance is \( u = -60 \, \text{cm} \) (since the object is placed at a distance of 60 cm in front of the concave lens).
(ii) In the absence of the lens, the rays would focus at the focal point of the lens, which is \( f = 25 \, \text{cm} \), since the focal length of the lens is 30 cm.