A contact lens is made of plastic with an index of repraction of 1.5 , The lens has an outer radius of eurvature ( convex) of 2 cm and an inner radius of curvature (concave ) of 4 cm .the focal length of the lens is;
1/F=(n-1) • (1/R1-1/R2)=
=(1.5-1) • (1/0.02-1/0.04)=
=0.5• (50-25)=12.5
F=0.08 m
To find the focal length of the lens, we can use the lens maker's formula, which is:
1/f = (n - 1) * ((1/R1) - (1/R2))
Where:
f is the focal length
n is the refractive index of the lens material
R1 is the radius of curvature of the first surface (in this case, the outer surface)
R2 is the radius of curvature of the second surface (in this case, the inner surface)
Given:
n = 1.5
R1 = 2 cm (positive for convex surfaces)
R2 = -4 cm (negative for concave surfaces)
Using the lens maker's formula, we have:
1/f = (1.5 - 1) * ((1/2) - (1/-4))
Simplifying this equation, we get:
1/f = 0.5 * (1/2 + 1/4)
1/f = 0.5 * (2/4 + 1/4)
1/f = 0.5 * (3/4)
1/f = 3/8
Now, to find the focal length:
f = 8/3
Therefore, the focal length of the lens is approximately 2.67 cm.