Question

लेंस का मेकर सूत्र सिद्ध कीजिए ​

Answer 1

लेंस मेकर फॉर्मूला व्युत्पन्न

नीचे हमने लेंस फॉर्मूले के व्युत्पन्न की ओर इशारा किया है।

पहली सतह

n2/v1-n2/v2=n2-n1/r………………………………………. 1

दूसरी सतह

N1/v-n2/v1=n1-n2/r2……………………… 2

1 और 2 हमें जोड़ने,

1/v-1/u = (n2/n1-1) [1/R1-1/R2]

भी

1/v-1/u=1/f

इसलिए, 1/f = (अपवर्तक सूचकांक-1) (1/R1-1/R2)

Answer 2

Answer:

$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$

Explanation:

We can say that, using the formula for refraction at a single spherical surface,

For the first surface,$\frac{n_{2}}{v_{1}}-\frac{r_{1}}{u}=\frac{n_{2}-r_{1}}{R_{1}}$..........(i)

For the second surface, $\frac{n_{1}}{v}-\frac{n_{2}}{v_{1}}=\frac{n_{1}-n_{2}}{R_{2}} \ldots(ii)$

Adding equation (1) and (2),

$\begin{aligned}&\frac{n_{1}}{v}-\frac{n_{1}}{u}=\left(n_{2}-n_{1}\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right] \\&\Rightarrow \frac{1}{v}-\frac{1}{u}=\left(\frac{n_{2}}{n_{1}}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]\end{aligned}$

$\text { When } u=\infty \text { and } v=f$

$\frac{1}{f}=\left(\frac{n_{2}}{n_{1}}-1\right)\left[\frac{1}{R_{1}}-\frac{1}{R_{2}}\right]$

Thenalso,

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Hence, we can say that,

$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$

Here μ is the refractive index of the material.