With the help of ray diagram, show the formation of image of a point object by refraction of light at a spherical surface separating two media of refractive indices n1 and n2 (n2 > n1) respectively. Using this diagram, derive the relation.n2v-n1u = n2-n1R What happens to the focal length of convex lens when it is immersed in water? - Zigya

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With the help of ray diagram, show the formation of image of a point object by refraction of light at a spherical surface separating two media of refractive indices n₁and n₂ (n₂ > n₁) respectively. Using this diagram, derive the relation.

$\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}$

What happens to the focal length of convex lens when it is immersed in water?

(i) AMB is a convex surface separating two media of refractive indices n₁ and n₂ (n₂> n₁). Consider a point object O placed on the principal axis. A ray ON is incident at N and refracts along NI. The ray along ON goes straight and meets the previous ray at I. Thus I is the real image of O.
$(i) AMB is a convex surface separating two media of refractive indice$

For Snell's law,

straight n subscript 2 space equals space fraction numerator sin space straight i over denominator sin space straight r end fraction

straight n subscript 1 space sin space straight i space equals space straight n subscript 2 space sin space straight r space space space space space space space straight n subscript 2 over straight n subscript 1 space equals space fraction numerator sin space straight i over denominator sin space straight r end fraction

or,

straight n subscript 1 straight i space equals space straight n subscript 2 straight r

From

increment space NOC comma space

straight i space equals space straight alpha space plus space straight gamma

From

increment space NIC comma

straight gamma space equals space straight r space minus space straight beta

or,

straight r space equals space straight gamma space minus space straight beta

therefore

straight n subscript 1 space left parenthesis straight alpha space plus space straight gamma right parenthesis space equals space straight n subscript 2 left parenthesis straight gamma space minus space straight beta right parenthesis

or

straight n subscript 1 straight alpha space plus space straight n subscript 2 straight beta space equals space left parenthesis straight n subscript 2 minus straight n subscript 1 right parenthesis space straight gamma

But

straight alpha space approximately equal to space tan space straight alpha space equals space NP over OP space equals space NP over OM

[P is close to M]

straight beta space approximately equal to space tan space straight beta space equals space NP over PI space equals space NP over MI

straight gamma space approximately equal to space tan space straight gamma space equals space space NP over PC space equals space NP over MC

therefore

straight n subscript 1. space NP over OM plus straight n subscript 2. space NP over MI space equals space left parenthesis straight n subscript 2 minus straight n subscript 1 right parenthesis space NP over MC

Or,

straight n subscript 1 over OM plus straight n subscript 2 over MI space equals space fraction numerator straight n subscript 2 minus straight n subscript 1 over denominator MC end fraction

Using Cartesian sign convention,

OM space equals space minus straight u comma space space space MI space equals space plus straight v comma space space space MC space equals space plus space straight R

therefore

fraction numerator straight n subscript 1 over denominator negative straight u end fraction plus straight n subscript 2 over straight v space equals space fraction numerator straight n subscript 2 minus straight n subscript 1 over denominator straight R end fraction

or,

box enclose straight n subscript 2 over straight v minus straight n subscript 1 over straight u space equals space fraction numerator straight n subscript 2 minus straight n subscript 1 over denominator straight R end fraction end enclose

Sign convention: Refer to Page 476.

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