# How can we change a camera from F/4 to F/5.6 ?

A) Increase the aperture to 2 times keeping the focal distance constant.

B) Increase the aperture to \[\sqrt 2 \] time keeping the focal distance constant.

C) Increase the aperture to \[\dfrac{1}{2}\] time keeping the focal distance constant.

D) Increase the aperture to $\dfrac{1}{{\sqrt 2 }}$ time keeping the focal distance constant.

Answer

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

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