Question

Find the focal length of the glass lens in FIGURE EX$34.25.$$34.25.$

Short answer

The focal length of the glass lens is$f=30\mathrm{cm}$

Step-by-step solution

Concepts and Principles

The optics' equation represents the reciprocal of the depth of field $f$of such a distorted lens covered by wind.

$\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

When utilizing the optics' equation, there are very few sign things to remember:

$1$. For edges which are convex it towards the target, the bending moment $R$is favorable.

$2$. The bending moment $R$is weak for screens wedge it towards the entity

Given Data

• We get a large glass lens with radius $40\mathrm{cm}\text{and}24\mathrm{cm}\text{.}$
  
• The crystal's reflection coefficient is:$n=1.50$
  

Required Data

The object distance of the optic should be specified.

Solution

If the object is on the left, the first surface is a domed surface$R_1=24\mathrm{cm}$with the a curved surface $R_2=-40\mathrm{cm}$. The lens' line of sight is then estimated using the lens maker's equation $"\text{Equation}{\left({}^{\ast }\right)}^n\text{:}$

$\frac{1}{f}=(n-1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$

$\frac{1}{f}=(1.50-1)\left(\frac{1}{24\mathrm{cm}}-\frac{1}{-40\mathrm{cm}}\right)$ (Numerically)

$\frac{1}{f}=\frac{1}{30\mathrm{cm}}$

$f=30\mathrm{cm}$