Question

Power of a lens of focal length \[1\,{\text{cm}}\] is
A. \[1\,{\text{D}}\]
B. \[10\,{\text{D}}\]
C. \[100\,{\text{D}}\]
D. \[\dfrac{1}{{100}}\,{\text{D}}\]

Answer 1

Hint:Use the formula for the power of a lens. This formula gives the relation between the power of lens and focal length of the lens. First convert the unit of focal length of the lens from the CGS system of units to the SI system of units and then substitute this value of focal length in the formula for power of the lens and calculate the power of the lens.

Formula used:
The formula for the power \[D\] of a lens is given by
\[D = \dfrac{1}{f}\] …… (1)
Here, \[f\] is the focal length of the lens.

Complete step by step answer:
We have given that the focal length of the lens is \[1\,{\text{cm}}\].
\[f = 1\,{\text{cm}}\]
We have asked to calculate the power of this lens.Let us first convert the unit of focal length of the lens from the CGS system of units to the SI system of units.
\[f = \left( {1\,{\text{cm}}} \right)\left( {\dfrac{{{{10}^{ - 2}}\,{\text{m}}}}{{1\,{\text{cm}}}}} \right)\]
\[ \Rightarrow f = {10^{ - 2}}\,{\text{m}}\]
\[ \Rightarrow f = 0.01\,{\text{m}}\]
Hence, the focal length of the lens in the SI system of units is \[0.01\,{\text{m}}\].
We can calculate the power of the lens using equation (1).Substitute \[0.01\,{\text{m}}\] for \[f\] in equation (1).
\[D = \dfrac{1}{{0.01\,{\text{m}}}}\]
\[ \therefore D = 100\,{\text{D}}\]
Therefore, the power of the given lens is \[100\,{\text{D}}\].

Hence, the correct option is C.

Note:The students should keep in mind that the focal length of the given lens is in the CGS system of units and the given options for the power of the lens are in the SI system of units. So, the students should not forget to convert the unit of focal length of the lens in the SI system of units. If one does not convert the unit of focal length then the final answer for the power of lens will be incorrect.