Chapter 23, Problem 46P

To determine

The type of lens, its focal length and the type of image (real/virtual).

Answer to Problem 46P

Solution:

It is converging lens with focal length 36.82cm and image will be virtual and inverted.

Explanation of Solution

Given:

Object distance, u= -155cm

Image distance, v=48.3cm

Formula used:

Lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

u and v are lens to object and lens to image distances respectively, negative when opposite to optical path and positive when in the direction of optical path.

Calculation:

Focal length of the lens can be calculated using the lens formula.

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Here value of u and v are given, i.e., $u=-\text{155cmand }v=\text{48}.\text{3cm}$.

Thus substituting them in formula we get-

$\begin{array}{l}\frac{1}{48.3}-\frac{1}{155}=\frac{1}{f}\\ \frac{1}{f}=\frac{48.3\times 155}{48.3+155}\\ f=36.82\text{cm}\end{array}$

It is a converging lens with positive power. Image will be virtual and inverted.