PHYSICS MODERN OPTICS Q There are two specks of dirt trappe

PHYSICS - MODERN OPTICS

Q: There are two specks of dirt trapped in a crystal ball: one at the center and the other halfway to the surface. If you peer into the ball on a line joining the two specks, the outer one appears to be only 1/3 of the way to the other. Determine the refractive index of the ball? [Hint: First use Gauss formula to find the location (in terms of R) of the image of the speck positioned at the center.]

Please show equation(s) and the steps leading up to the answer

Thx =)

Solution

We know that gaussian lens formula as n/d_object=1/f+ n/d_image

here n is the refrative index of the ball.

Now, for first object, one on halfway to surface, 2*n/R=1/R+ n/d_image1;

for second object, one on centre; n/R = 1/R +  n/d_image2

That is for object1, (2n -1)/n = 3*R/d_image2 [The first object appears to be at 1/3rd of the distance of second one]

for object2, (n-1)/n = R / d_image2

Dividing first equation above by the second, we get:

(2n - 1)/(n-1) = 3

That is, n = 2