Question

Two thin convex lens of power + 5 diopter and + 4 diopter are placed coaxially at a distance 10 cm find the focal length of the combination

Answer 1

Answer: The focal length of the combination is  0.14.

Explanation:

The expression of the power in terms of focal length is as follows;

$P=\frac{1}{f}$

Here, f is the focal length and P is the power.

Calculate the focal length for the  convex length having having power of +5D.

$P_1=\frac{1}{f_1}$

Put P_1 = +5 D.

$5=\frac{1}{f_1}$

${f_1}=\frac{1}{5}$  

Similarly, calculate the focal length for the  convex length having having power of +4D.

$P_2=\frac{1}{f_2}$

Put P_2= +4 D.

$5=\frac{1}{f_{2}}$

${f_{2}}=\frac{1}{4}$  

The expression for the focal length of the combination of the lens is as follows;

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{(f_1)(f_2)}$

Convert the cm into m.

d= 10 cm = 0.1 m.

Put

$\frac{1}{f_{1}}=5$

$\frac{1}{f_{2}}=4$

d=0.1 m.

$\frac{1}{f}=5+4-\frac{0.1}{(5)(4)}$

$f=0.14 m$

Therefore, the focal length of the combination is  0.14.

Answer 2

Explanation:

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