Question

A lens of focal length 45 mm is mounted on a 35-mm camera. The lens aperture is set at f/2.0 and the shutter speed set at 1/2000 s. The photographer wants to keep the same exposure (amount of light), but wants to change the f-number to f/8.0 for greater depth of field. What should be the new shutter speed to maintain the same exposure? Please show steps so I can understand the problem.

Answer 1

Focal length of the lens is f = 45 mm

Focal length is constant and does not change.

Diameter of the lens D = focal length / f number

D1 = f / f_n1 = f / 2.0

Shutter speed t1 = ( 1 / 2000 ) s

f number is changed to 8.0 , then the diameter is D2 = f / 8.0

Let this new f number as   f_n2 = 8.0

We have to calculate the shutter speed t2 when the f number is 8.0

Exposure to the light is proportional to area of the lens and time.

E   A t

Area is proportional to square of the diameter . So we can write

E D² × t

We know that diameter D = f / f_n ,

E   t × ( f / f_n )²

Exposure and focal length are same so we can write ,

t1 / (f_n1 )² = t2 / ( f_n2 )²

t2 = t1 × ( f_n2 / f_n1 )²

= ( 1 / 2000 ) × ( 8.0 / 2.0 )²

= 64 / ( 2000 × 4 )

= ( 1 / 125 ) s

So the shutter speed reduces to 1/125 per second.