Question

An eye specialist prescribes a spectacles having a combination of convex lens focal length 40cm in contact with a concave lens of focal length 25cm. the power of this combination of lens in diopter is
A. + 1.5
B. – 1.5
C. + 6.67
D. – 6.67

Answer 1

Hint: We have given the focal length of convex and concave lens, so we will find the power of both the lenses by using the formula Power = $\dfrac{{100}}{{f(incm)}}$. As it is given that the two lenses are in contact, therefore, the separation between them is zero. Therefore using formula for power of combination of lenses ${P_{net}} = {P_1} + {P_2} - d{P_1}{P_2}$ we can find the required answer.

Complete step-by-step answer:
Now, from the question, given
Focal length of convex lens = ${f_1}$ = + 40cm
Focal length of concave lens = ${f_2}$ = - 25cm
And as the lenses are in contact so separation between them is, d = 0
Power of the lens can be given as
Power = $\dfrac{{100}}{{f(incm)}}$
Power of combination of lens can be given as:
${P_{net}} = {P_1} + {P_2} - d{P_1}{P_2}$
${P_{net}} = \dfrac{{100}}{{40}} - \dfrac{{100}}{{25}} - 0$
= 2.5 – 4
= - 1.5D
${P_{net}}$ = - 1.5D
So the correct option is B.

Note: Simply put, the ability of a lens in Ray Optics is its ability to bend light. The greater the power of a lens, the greater is its ability to refract light that passes through it. For a convex lens, the converging ability is defined by power and in a concave lens, the diverging ability. To find the ability of a lens in Ray Optics, the subsequent formula are often used
Power = $\dfrac{{100}}{{f(incm)}}$
If the focal length is given in meters (m), the power of the lens if measured in Diopters (D), as in the unit of power of the lens is diopter. Another thing you should keep in mind is that for a converging lens the optical power is positive and for a diverging lens, it is negative.