Question

In an optical bench experiment index error is \[ + 1\,{\text{cm}}\] and \[ - 1\,{\text{cm}}\], between object needle and lens, lens and image needle respectively. Observed values of u and v are \[9\,{\text{cm}}\]and \[17\,{\text{cm}}\]. Focal length of lens is closest to:-
A. \[{\text{6}}{\text{.15 cm}}\]
B. \[{\text{5}}{\text{.54 cm}}\]
C. \[{\text{5}}{\text{.88 cm}}\]
D. \[{\text{6}}{\text{.25 cm}}\]

Answer 1

Hint: For this question, use the lens formula to find out the focal length of the lens.
 In the lens formula put the values of u and v to get the value of focal length of lens.

Complete step by step answer:
Given, distance between needle and the lens, \[u = - {\text{9cm}}\]
(the negative sign is because of the sign convention)
Distance between image and the lens, \[v = 17{\text{cm}}\]
From the lens formula we have,
\[\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}\]...............................(1)
Where \[u\] is the distance between object and the lens and \[v\] is the distance between image and the lens and \[f\] is the focal length of the lens.
Putting the values of \[u\] and \[v\] in equation (1), we get
\[\dfrac{1}{{17}} - \dfrac{1}{{\left( { - 9} \right)}} = \dfrac{1}{f}\]
\[ \Rightarrow \dfrac{1}{f} = \dfrac{{26}}{{153}}\]
\[ \Rightarrow f = \dfrac{{153}}{{26}} = 5.88\,{\text{cm}}\]
Therefore, focal length of the lens is closest to \[5.88\,{\text{cm}}\].

So, the correct answer is “Option C”.

Note:
While solving such questions in which we have to use lens or mirror formulas take care of the sign convention, the distance from the left of the lens or mirror are taken negative and distances taken from the right are taken as positive.
Optics Bench provides the basic knowledge about properties of light such as Refraction, Reflection, Dispersion and Total internal reflection.