A very long 1.75 cm diameter glass rod has one end ground and polished to a convex spherical surface that has a 7.30 cm radius. The glass material has an index of refraction 1.56.
To find the focal length of the glass rod lens, we can use the lens maker's formula:
1/f = (n - 1) * ((1/R1) - (1/R2))
Where:
- f is the focal length of the lens
- n is the refractive index of the material (given as 1.56)
- R1 is the radius of curvature of the first surface (given as 7.30 cm)
- R2 is the radius of curvature of the second surface, which is essentially infinity for a long rod lens
Since the radius of curvature for the second surface is very large (essentially infinity), we can assume that 1/R2 ≈ 0.
Plugging in the values into the formula:
1/f = (1.56 - 1) * ((1/7.30) - 0)
Simplifying:
1/f = (0.56) * (1/7.30)
1/f ≈ 0.0767 cm^-1
To find the focal length, take the reciprocal of both sides:
f ≈ 13 cm
So, the approximate focal length of the glass rod lens is 13 cm.