Question

What is meant by power of a lens? Define its SI unit.
You have two lenses A and B of focal lengths \[ + 10cm\] and $ - 10cm$ respectively. State the nature and power of each lens. Which of the two lenses will form a virtual and magnified image of an object placed $8cm$ from the lens? Draw a ray diagram to justify your answer.

Answer 1

Hint: Convert the given data in the SI units and solve using applicable formulas. The power of a lens is the measure of the amount of the deviation of the light ray produced by the lens. It is inversely proportional to the focal length. i.e. $P = \dfrac{1}{f}$

Complete step by step answer:
Power of lens – The ability of the lens to converge or to diverge the rays of the light falling on it.
The power of a lens is also defined as the reciprocal of the focal length. The more powerful lens has a shorter focal length. The converging (convex) lenses have the positive focal lengths and so they also have positive power values whereas, the diverging (concave) lenses have the negative focal lengths, and so they also have the negative power values.
It can be expressed as –
$
  power{\text{ of lens = }}\dfrac{1}{{focal\,{\text{length}}}} \\
  P = \dfrac{1}{f} \\
  1\,{\text{Dioptre = }}\dfrac{1}{{meter}} \\
 $
Power of the lens is measured in the dioptres (D).
Now, Given that –
The focal length of the lens A, ${f_A} = + 10cm = 0.1m$ (According to the conversion ratio$100cm = 1m$)
The focal length of the lens B, ${f_B} = + 10cm = 0.1m$
Power of lens A, ${P_A} = \dfrac{1}{{ + 0.1}}$
$\therefore {P_A} = + 10D$
As the power of lens A is positive, the lens is a converging lens or the convex lens.
Similarly find power of lens B.
Power of lens B, ${P_B} = \dfrac{1}{{ - 0.1}}$
$\therefore {P_B} = - 10D$
As, the power of the lens is negative and therefore it is the diverging lens or concave lens.
Also, given that the object is placed at $8cm$ from the lens, which is at the distance less than $10cm$
In the convex lens, when the object is placed between the pole and the focus, the image formed is always virtual and diminished.
Hence, the lens will create a virtual and magnified image of the object.
The required ray diagram is as shown below –

Note:
 Apply conversion of units where applicable to solve these types of problems. You cannot simplify equations with different units. The convex lens has positive power and the concave lens has the negative power. The power of a plane glass plate is always zero. The power of the combinations of the lenses kept close to each other is equal to the sum of the individual power of each of the lenses.