Question

Which of the following graph represents the relation between the image position {v) and object position (u) from the concave lens.

Answer 1

We have to check which of the following graph represent the relation between the image (v) and object position (u) from the concave lens (f).

Solution : let's take a concave lens of focal length f, and object is placed at u distance from the lens and image forms v distance from the lens.

from lens maker formula,

1/v - 1/u = 1/-f

differentiating with respect to u

-1/v² dv/du + 1/u² = 0 [ f is constant term so df/du = 0]

⇒dv/du = v²/u²

here it is clear that slope of graph v and u must be positive.

only options (1) and (4) have positive slopes.

but we see centre of hyperbola is (-2f , 2f) , so option (4) is correct not option (1).

Therefore correct option is (4)