Answer

Verified

347.7k+ views

**Hint:**The formulae such as, the lens formula, that relates the focal length, the object distance and the image distance, the power formula, that relates the focal length and the power of the lens should be used to solve this problem.

**Formula used:**

\[\begin{align}

& \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\

& P=\dfrac{1}{f} \\

\end{align}\]

**Complete step by step answer:**

From the given information, we have the data as follows.

A certain far-sighted person cannot see objects closer to the eye than 100 cm. The distance of 25 cm.

As the values of the image distance and the object distance are given, so, we will be using the formula that relates the focal length, the object distance and the image distance, the reason being, the inverse of the focal length gives the power of the lens.

Consider the lens formula.

\[\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}\]

Substitute the values of the image distance and the object distance in the above equation.

\[\dfrac{1}{f}=\dfrac{1}{-100}-\dfrac{1}{-25}\]

Continue further computation.

\[\begin{align}

& \dfrac{1}{f}=\dfrac{1}{-100}+\dfrac{1}{25} \\

& \therefore \dfrac{1}{f}=\dfrac{3}{100}cm \\

\end{align}\]

Thus, the value of the focal length is,

\[\begin{align}

& \dfrac{1}{f}=\dfrac{3}{100} \\

& \Rightarrow \dfrac{1}{f}=\dfrac{3}{100}c{{m}^{-1}} \\

& \therefore f=\dfrac{1}{3}m \\

\end{align}\]

The power formula that relates the power of the lens and the focal length of the lens is given as follows.

Consider the lens formula.

\[P=\dfrac{1}{f}\]

Substitute the value of the focal length in the above equation.

\[P=\dfrac{1}{{}^{1}/{}_{3}}\]

Thus, the value of the power of the lens is,

\[P=3\,D\]

\[\therefore \] The power of the lens which will enable a certain far-sighted person to read at a distance of 25 cm will be 3 dioptres.

**So, the correct answer is “Option A”.**

**Note:**The lens formula gives the relation between the focal length, the image distance and the object distance, the mirror formula gives the relation between the focal length, the image distance and the object distance, but, the difference being the sign used (+/-).

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Guru Purnima speech in English in 100 words class 7 english CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Select the word that is correctly spelled a Twelveth class 10 english CBSE