Chapter 12.7, Problem 8P

To determine

To calculate: The radius of the lens for an exposure time of 0.0025 s , if the lens of radius 1 cm is taking 0.01 s of exposure time , also given the exposure time needed for a photograph is inversely proportional to the square of the radius of the camera lens.

Answer to Problem 8P

The radius of the lens is $r=2cm$

Explanation of Solution

Given information:

The exposure time needed for a photograph is inversely proportional to the square of the radius of the camera lens.

Let, r is the radius of the lens

t is the exposure time

So $t\prec \frac{1}{r^2}$

Let k be a constant

  $t=\frac{k}{r^2}$.............. (1)

Put the value of t and r in equation 1 to get the value of k .

  $0.01s=\frac{k}{{\left(1\right)}^2}$

Solve further to get k ,

  $k=0.01$

Now, put the value of t and k in equation 1 to get r ..

  $t=\frac{k}{r^2}$

  $0.0025s\text{}=\frac{0.01}{r^2}$

  $r^2=\frac{0.01}{0.0025}$

  $r=\sqrt{\frac{0.01}{0.0025}}$

After solving,

  $r=\sqrt{\frac{1}{100}\times \frac{10000}{25}}$

  $r=\sqrt{4}$

  $r=2cm$