Question

Derive equation for convex surface if object is in rarer Med. and image is also in rarer medium​

Answer 1

Answer:

Refer to the above attachment

Explanation:

Hope it helps you

Answer 2

Explanation:

one medium (rarer) and on the right side the second medium (denser). P is the pole of the spherical surface and C is its centre of curvature. According to ray diagram of fig, I is the image of the object O. The normal drawn from point M on principal axis is MP’.

According to Snell's law,

1n2=sinrsini

where 1n2 = the refractive index of medium (2) with respect to medium (1).

n=sinrsini

(on taking n in place of 1n2 temporarily ) If the angles i and r are very small, then

sini≈i and sin≈r

∴n=ri

or i=nr ...........(1)

∴ In triangle, the exterior angle is equal to sum of the opposite two interior angles.

∴ From ΔMOC,i=α+γ ..........(2)

And from ΔMIC,

r=β+γ ...........(3)

Substituting the value of i and r in equation (1), then we get,

(α+γ)=n(β+γ) ............(4)

If point M is not far from the principal axis, then 

(i) Points P and P' are very close to each other and considered to be same point.

(ii) Angles α,β and γ will be small.

Therefore, α≈tanα=OPMP=−uMP

β=tanβ=IPMP=−vMP

and γ=tanγ=CPMP=RMP

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