SATHEE: Optics 3 Question 12

Optics 3 Question 12

12. A thin convex lens made from crown glass $(μ = 3 / 2)$ has focal length $f$ . When it is measured in two different liquids having refractive indices $4 / 3$ and $5 / 3$ . It has the focal lengths $f_{1}$ and $f_{2}$ , respectively. The correct relation between the focal length is

(2014 Main)

(a) $f_{1} = f_{2} < f$

(b) $f_{1} > f$ and $f_{2}$ becomes negative

(d) $f_{1}$ and $f_{2}$ both become negative

Show Answer

Answer:

Correct Answer: 12. (b)

Solution:

It is based on lens maker’s formula and its magnification.

$i.e. \frac{1}{f} = (μ - 1) \frac{1}{R_{1}} - \frac{1}{R_{2}}$

According to lens maker’s formula, when the lens in the air

$\begin{aligned} \frac{1}{f} = \frac{3}{2} - 1 \frac{1}{R_{1}} - \frac{1}{R_{2}} \\ \frac{1}{f} = \frac{1}{2 x} \Rightarrow f = 2 x \end{aligned}$

$Here, \frac{1}{x} = \frac{1}{R_{1}} - \frac{1}{R_{2}}$

In case of liquid, where refractive index is $\frac{4}{3}$ and $\frac{5}{3}$ , we get

Focal length in first liquid

$\frac{1}{f_{1}} = \frac{μ_{s}}{μ_{l_{1}}} - 1 \frac{1}{R_{1}} - \frac{1}{R_{2}} \Rightarrow \frac{1}{f_{1}} = \frac{\frac{3}{2}}{\frac{4}{3}} - 1 \frac{1}{x}$

$\Rightarrow f_{1}$ is positive.

$\begin{aligned} \frac{1}{f_{1}} & = \frac{1}{8 x} = \frac{1}{4 (2 x)} = \frac{1}{4 f} \\ \Rightarrow & f_{1} & = 4 f \end{aligned}$

Focal length in second liquid

$\frac{1}{f_{2}} = \frac{μ_{s}}{μ_{l_{2}}} - 1 \frac{1}{R_{1}} - \frac{1}{R_{2}}$

$\Rightarrow \frac{1}{f_{2}} = \frac{\frac{3}{2}}{\frac{5}{3}} - 1 \frac{1}{x}$

$\Rightarrow f_{2}$ is negative.

पिछला

अगला

Optics 3 Question 12

12. A thin convex lens made from crown glass $(μ = 3 / 2)$ has focal length $f$ . When it is measured in two different liquids having refractive indices $4 / 3$ and $5 / 3$ . It has the focal lengths $f_{1}$ and $f_{2}$ , respectively. The correct relation between the focal length is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Optics 3 Question 12

12. A thin convex lens made from crown glass (μ=3/2) has focal length f. When it is measured in two different liquids having refractive indices 4/3 and 5/3. It has the focal lengths f1 and f2, respectively. The correct relation between the focal length is

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Menu

12. A thin convex lens made from crown glass $(μ = 3 / 2)$ has focal length $f$ . When it is measured in two different liquids having refractive indices $4 / 3$ and $5 / 3$ . It has the focal lengths $f_{1}$ and $f_{2}$ , respectively. The correct relation between the focal length is