# Air bubble inside a glass sphere problem

1. Jun 8, 2006

### Amith2006

Sir,
# A small air bubble in a sphere of 8 cm diameter of a substance having refractive index 1.4 appears to be 2 cm from the surface when looking along the diameter. Find the true position of the bubble.
I solved it in the following way:
Here n1 = 1, n2 = 1.4, v = -2 cm(Virtual image), R = + 4 cm
n2/v + n1/u = (n2 – n1)/R
1.4/-2 + 1/u = 0.4/4
1/u = 0.1 + 0.7 = 0.8
u = 1/0.8
u = 1.25 cm
But the book answer is 2.33 cm. But I get this answer if I do it in a different way.
Here n1 = 1, n2 = 1.4, v = -2 cm(Virtual image), R = + 4 cm
n1/v + n2/u = (n1 – n2)/R
1/-2 + 1.4/u = (1.4 – 1)/4
1.4/u = 0.1 + 0.5 = 0.6
u = 1.4/0.6
u = 2.33 cm

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2. Jun 8, 2006

### Staff: Mentor

I don't understand this solution; seems like you mixed up n1 and n2.
I'd say that you made two errors in this one that counterbalance each other. (Unless I'm misreading what you've done.)

Using the usual (Halliday & Resnick) sign convention, the equation you need is:
n1/u + n2/v = (n2 - n1)/R
where u = object distance; v = image distance

Since the light from the object goes from inside the sphere to outside, n1 = 1.4 & n2 = 1. Also, since the surface as the light hits it is concave, R = -4 cm. Given is that v = - 2 cm (a virtual image). Solve for u, the object distance.