Question

What radius of curvature must the two spherical surfaces of a biconvex lens with surfaces having equal radii be ground so that the focal length will be 85 mm if the glass has a refractive index of 1.570?

Answer 1

Answer 2

we can use the Lensmaker's Formula for a lens with equal radii (let's call the radius $R$):

$$\frac{1}{f}=(n-1)\left(\frac{2}{R}\right)$$

Where:

• $f$ is the focal length (85 mm).

• $n$ is the refractive index of the glass (1.570).

• $R$ is the radius of curvature for both surfaces.

 

1. Plug in the known values:

   $$\frac{1}{85}=(1.570-1)\left(\frac{2}{R}\right)$$

2. Simplify the equation:

   $$\frac{1}{85}=0.570\times \left(\frac{2}{R}\right)$$

3. Further simplify:

   $$\frac{1}{85}=\frac{1.140}{R}$$

4. Solve for $R$:

   $$R=1.140\times 85$$$$R=96.9\text{ mm}$$

Answer is :

The radius of curvature for each spherical surface of the biconvex lens must be approximately 96.9 millimeters.