Question

a double convex lens of focal length 20 cm is made of glass of refractive index 2/3.when placed completely in water(a M w) its focal length will be..
1) 80cm. 2) 15cm. 3) 17.7cm. 4) 22.5cm

Answer 1

Answer on Question #52354, Physics, Optics

A double convex lens of focal length $20\mathrm{cm}$ is made of glass of refractive index $3/2$. When placed completely in water ($a\mu_w = 4/3$) its focal length will be..

1) $80\mathrm{cm}$. 2) $15\mathrm{cm}$. 3) $17.7\mathrm{cm}$. 4) $22.5\mathrm{cm\_w}$

Solution:

The focal length of a lens can be calculated from the lensmaker's equation:

$$\frac{1}{f} = \frac{(\mu_2 - \mu_1)}{\mu_1} \left(\frac{1}{R_1} - \frac{1}{R_2}\right)$$

In first case (lens in air)

$$\frac{1}{f_a} = \frac{(3/2 - 1)}{1} \left(\frac{1}{R} + \frac{1}{R}\right)$$

In first case (lens in water)

$$\frac{1}{f_w} = \frac{(3/2 - 4/3)}{4/3} \left(\frac{1}{R} + \frac{1}{R}\right)$$ $$\frac{f_w}{f_a} = \frac{\left(\frac{3}{2} - 1\right)}{\frac{3}{2} - \frac{4}{3}} \cdot \frac{4}{3} = 4$$ $$f_w = 4 \cdot f_a = 4 \cdot 20\ \mathrm{cm} = 80\ \mathrm{cm}$$

Answer: 1) $80\mathrm{cm}$

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