(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)
S safeer

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}

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