A planoconvex lens is to have a focal length of 28.5 cm. If made from fused quartz, what must be the radius of curvature of the convex surface?
Use the so-called "lens maker's formula" and an index of refraction of N = 1.458 for fused quartz.
1/f = (N-1)/R1 (for a plano-convex lens with R2 = infinity on one side)
Solve for R1.
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenmak.html
To determine the radius of curvature of the convex surface of a planoconvex lens, we can use the lens-maker's formula. The lens-maker's formula relates the focal length of a lens (f), the refractive index of the lens material (n), and the radii of curvature of its surfaces (R1 and R2).
The formula is given as:
1/f = (n - 1) * [(1/R1) - (1/R2)]
In this case, the lens is made from fused quartz. The refractive index of fused quartz is approximately 1.46, so we can substitute this value into the formula. Also, since one surface of the lens is a plane (zero radius of curvature), we can substitute R1 as infinity.
Hence, the formula becomes:
1/28.5 = (1.46 - 1) * [(1/infinity) - (1/R2)]
Since the reciprocal of infinity is zero, we can simplify the formula:
1/28.5 = 0.46/R2
To find R2, we rearrange the equation:
R2 = 0.46 * 28.5
R2 ≈ 13.11 cm
Therefore, to achieve a focal length of 28.5 cm for a planoconvex lens made from fused quartz, the radius of curvature of the convex surface should be approximately 13.11 cm.