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  • (a) Two thin lenses are placed coaxially in contact. Obtain the expression for the focal length of this combination in terms of the focal lengths of the two lenses. (b) A converging lens of refractive index 1.5 has a power of 10 D. When it is

(a) Two thin lenses are placed coaxially in contact. Obtain the expression for the focal length of this combination in terms of the focal lengths of the two lenses.

(b) A converging lens of refractive index 1.5 has a power of 10 D. When it is completely immersed in a liquid, it behaves as a diverging lens of focal length 50 cm. Find the refractive index of the liquid.

 

 
 
 
 
 

Answers (1)

a) 

For image I_{1} by L_{1}

\frac{1}{V_{1}}=\frac{1}{u}+\frac{1}{f_{1}}

\frac{1}{V_{1}}-\frac{1}{u}=\frac{1}{f_{1}}\; \; \; \; \; \; -----(1)

For image I by lens L_{2}

\frac{1}{V}-\frac{1}{V_{1}}=\frac{1}{f_{2}}\; \; \; \; ------(2)

(1)+(2)

\Rightarrow \frac{1}{V}-\frac{1}{u}=\frac{1}{f_{1}}+\frac{1}{f_{2}}

Considering the two lenses to be a single lens of focal length f then,

\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}

b)

P_1=(_a \mu_g-1)[1/R_1-1/R_2]

P_2=(_l \mu_g-1)[1/R_1-1/R_2]

\frac{P_1}{P_2}=\frac{(_a \mu_g-1)}{(_l \mu_g-1)}

\\\frac{10}{-2}=\frac{1.5-1}{\frac{1.5}{\mu_l}-1}\\\mu_l=\frac{5}{3}

Posted by

Safeer PP

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