Answer

Verified

386.4k+ views

**Hint:**Since the power is positive, the lens used is a convex lens. The power is the reciprocal of focal length, so we can calculate the focal length. Using the lens formula and substituting corresponding values we can find the image distance which is the minimum distance at which objects must be kept so that the man can see clearly without glasses.

**Formulas used:**

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

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

**Complete answer:**

It is clear that the man is far-sighted, this means he suffers from Hypermetropia and cannot see nearby objects clearly. The lens of a certain power helps by creating a virtual image of the object at a distance where it is clearly visible to the man.

Therefore, the least distance at which the man must hold the newspaper is $25cm$ therefore, the least distance where he can see objects clearly can be calculated using the lens formula-

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$ - (1)

Here, $v$ is the image distance

$u$ is the object distance

$f$is the focal length

For the condition given above, $u=-25cm$, the focal length is

$\begin{align}

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

& \Rightarrow f=\dfrac{100}{3}cm \\

\end{align}$

We substitute given values in eq (1) to get,

$\begin{align}

& \dfrac{1}{v}+\dfrac{1}{25}=\dfrac{3}{100} \\

& \Rightarrow \dfrac{1}{v}=\dfrac{3}{100}-\dfrac{1}{25} \\

& \Rightarrow \dfrac{1}{v}=\dfrac{-1}{100} \\

& \therefore v=-100cm=-1m \\

\end{align}$

The minimum distance at which the man can see objects is $1m$.

Therefore, in order for the man to see objects clearly without glasses, the minimum distance at which objects must be kept is $1m$.

**Hence, the correct option is (D).**

**Note:**

By convention, all distances from left to right are taken as negative and distances from right to left are taken as positive. Therefore, object distance is always negative. Here, image distance is negative because the image formed is virtual. To correct Hypermetropia, convex lenses are used.

Recently Updated Pages

Which of the following is correct regarding the Indian class 10 social science CBSE

Who was the first sultan of delhi to issue regular class 10 social science CBSE

The Nagarjuna Sagar project was constructed on the class 10 social science CBSE

Which one of the following countries is the largest class 10 social science CBSE

What is Biosphere class 10 social science CBSE

Read the following statement and choose the best possible class 10 social science CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

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

Difference Between Plant Cell and Animal Cell

Why is the Earth called a unique planet class 6 social science CBSE