Chapter 25, Problem 61GP

To determine

The object distance and the distance between the object and the film.

Answer to Problem 61GP

The distance of object is $100mm$ .

The distance between the object and the film is $200mm$ .

Explanation of Solution

Given info:

The focus length, $f=50mm$

Formula used:

  $\frac{\text{1}}{{\text{d}}_{\text{o}}}\text{ + }\frac{\text{1}}{{\text{d}}_{\text{i}}}\text{ = }\frac{\text{1}}{\text{f}}$

Where,

  $\text{f}$ is a focal length.

  ${\text{d}}_{\text{o}}$ is distance from the source to lens. 

  ${\text{d}}_{\text{i}}$ is distance from the screen to the lens.

Calculation:

As ${\text{h}}_{\text{i}}{\text{=h}}_{\text{o}}$ , magnification, $\text{m =}\frac{{\text{h}}_{\text{i}}}{{\text{h}}_{\text{o}}}\text{=-}\frac{{\text{d}}_{\text{i}}}{{\text{d}}_{\text{o}}}\text{=-1}$

So, ${\text{d}}_{\text{i}}{\text{=d}}_{\text{o}}$

Now, calculate the object distance from $\frac{\text{1}}{{\text{d}}_{\text{o}}}\text{ + }\frac{\text{1}}{{\text{d}}_{\text{i}}}\text{ = }\frac{\text{1}}{\text{f}}$

  $\frac{\text{1}}{{\text{d}}_{\text{o}}}\text{ + }\frac{\text{1}}{{\text{d}}_{\text{i}}}\text{ = }\frac{\text{1}}{\text{50}\text{mm}}$

  ${\text{d}}_{\text{o}}\text{=100}\text{mm}$

Now calculate the distance between an object and the film

  $d=d_o+d_i$

  $d=100mm+100mm=200mm$

Conclusion: The distance of object is $100mm$ .

The distance between the object and the film is $200mm$ .