Question

A thin double convex lens have surfaces of radii of curvature 30 cm each.Find the Refractive index of the material of lens if the focal length is 25 cm ​

Answer 1

Answer:

For the double convex lens

f=25cm,R1=R and R2=−2R  (sign convention)  

f1=(μ−1)(R11−R21)  

⇒251=(15−1)(R1−−2R1)=0.5(23R)  

⇒251=43R1⇒R=18.75cm  

R1=18.75cm,R2=2R=37.5cm  

Answer 2

Concept Introduction: Numericals on Lenses are the most basic concepts in Physics.

Given:

We have been Given:

$f = 25cm$

$r1 = 30cm \: \: and \: \: r2 = - 2 \times 30$

To Find:

We have to Find: The refractive index.

Solution:

According to the problem, We know by the Lens Maker's Formula that,

$\frac{1}{f} = (u - 1)( \frac{1}{r1} - \frac{1}{r2} )$

therefore putting the values, we get,

$\frac{1}{25} = (u - 1)( \frac{1}{30} + \frac{1}{60} ) \\ \frac{1}{25} = (u - 1)( \frac{60 + 30}{1800} ) \\ \frac{1}{25} = (u - 1) \times \frac{90}{1800} \\ \frac{20}{25} = (u - 1) \\ \frac{20}{25} + 1 = u \\ u = \frac{20 + 25}{25} \\ u = \frac{45}{25} \\ u = 1.8$

Final Answer: The Refractive index is

$1.8$

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