Air bubble inside a glass sphere problem

[Amith2006]

Sir,
Please help me with this problem.
# 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

 

[Doc Al]

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

I don't understand this solution; seems like you mixed up n1 and n2.

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

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.

 

[kyle8921]

Hello,

Thank you for reaching out for help with this problem. It seems that you have approached the problem correctly, but your calculations may have a small error in them. I would suggest double-checking your calculations and make sure you are using the correct values for n1 and n2 (which you have listed as 1 and 1.4, but in the equations, you have used 1 and 1.4 as well). Also, make sure you are using consistent units throughout your calculations.

If you still cannot find the error in your calculations, I would recommend seeking help from a colleague or your teacher to review your work and see if they can spot any errors. It is also possible that the book answer may be incorrect, so it's always good to double-check with another source.

I hope this helps and good luck with your future problem-solving!