Answer

Verified

419.7k+ views

**Hint:**For solving this question, we have to use the concept of f-number or focal ratio which is the ratio of the system’s focal distance to the diameter of aperture.

${\text{N = }}\dfrac{f}{D}$

Where, N is the f- number, D is the diameter of the aperture and f is the focal distance.

**Complete step by step answer:**

Let us first understand this concept of f-number. The formula is given by :-

${\text{N = }}\dfrac{f}{D}$ ……. (1)

where N is the f-number, f is the focal distance and D is the diameter of aperture of the camera. The f-number (N) is represented by F/N.

Now, in the question given above we have to convert a camera from F/4 to F/5.6. Hence, it’s f-number changes from 4 to 5.6.

For F/4 camera, let’s ${{\text{D}}_1}$ be its diameter of aperture and f-number is 4, so using the equation (1),

$4\, = \,\dfrac{f}{{{{\text{D}}_1}}}$ …….(2)

For F/5.6 camera, let’s \[{{\text{D}}_2}\] be it’s diameter of aperture and f-number is 5.6, so using the equation (1),

$5.6\, = \,\dfrac{f}{{{{\text{D}}_2}}}$ …….(3)

Since the focal distance is constant in both the cases, we will equate the equations (2) and (3) as,

$\implies 4 \times {{\text{D}}_1}\, = \,\,5.6 \times {{\text{D}}_2} \\

\implies \dfrac{{{{\text{D}}_1}}}{{{{\text{D}}_2}}}\, = \,\,\dfrac{{5.6}}{4} \\

\implies \dfrac{{{{\text{D}}_1}}}{{{{\text{D}}_2}}}\, = \,\,\sqrt 2 \\

\therefore {{\text{D}}_2}\, = \,\,\dfrac{{{{\text{D}}_1}}}{{\sqrt 2 }} \\

$

Hence, the diameter of aperture of the F/5.6 camera should be $\dfrac{1}{{\sqrt 2 }}$ time the diameter of the aperture of the F/4 camera keeping the focal distance constant.

**Therefore, (D) option is correct.**

**Note:**The f-number explains the light gathering ability of lens only for the objects at an infinite distance away. In some cases, a working f-number is used. But make sure to use the correct formula because many students assume the formula to be $f = \dfrac{N}{D}$ instead of ${\text{N = }}\dfrac{f}{D}$

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

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

Advantages and disadvantages of science

10 examples of friction in our daily life

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

10 examples of law on inertia in our daily life

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

In 1946 the Interim Government was formed under a Sardar class 11 sst CBSE

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