Question

Two lenses of power +2.50D and−3.75D are combined to form a compound lens Its focal length in cm will be
A. 40
B. -40
C. -80
D. 160

Answer 1

Hint: Lens are the things which will allow the light to pass through them with convergence or divergence. Depending on whether the lens will converge or diverge the rays they are divided into convex and concave lenses. Their capacity of convergence or divergence is given by power of the lens.

Formula used:
$\eqalign{
  & P = {P_1} + {P_2} \cr
  & P = \dfrac{1}{f} \cr} $

Complete step by step answer:
The main difference between the lens and mirrors is there are many ways to change the effective focal length of a lens without varying them geometrically. For example if we put the lens in a different medium from air then the refractive index in that medium will be different than that of air. This is not possible for mirrors. They have constant focal length and don’t vary with the medium.
This is because the rays will suffer refraction in the lens and that refraction depends upon the surrounding medium and the entering medium. In case of mirrors there will be no refraction hence the focal length of the mirror won’t change.
Power of the lens is given by the inverse of the focal length. When two lenses are brought very close to each other then their powers will add up and focal length will vary and we get effective focal length of the new lens.
$P = {P_1} + {P_2}$
$\eqalign{
  & \Rightarrow P = 2.5 - 3.75 \cr
  & \Rightarrow P = - 1.25 \cr
  & \Rightarrow P = \dfrac{1}{f} \cr
  & \Rightarrow - 1.25 = \dfrac{1}{f} \cr
  & \Rightarrow f = - 0.8m \cr
  & \therefore f = - 80cm \cr} $
Hence option C will be the answer.

Note:
The lens refractive index can be varied in such a way that a convex lens can behave as the concave lens without any change in shape. This is when we place the lens in the medium of refractive index greater than the lens refractive index, then the convex lens would change into concave while the concave lens would change into convex.