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;
Use the Lens Maker's formula, which is
1/f = (n-1)[(1/R1) - (1/R2)]
= 0.5 [(1/2) -(1/4)]
= 0.5 [1/4) = 1/8 cm^-1
f = 8 cm
where f is the focal length, n is the index of refraction, and R1 and R2 are the radii of curvature of the two sides of the lens. (R1 is convex and R2 is concave)
ref.:
http://scienceworld.wolfram.com/physics/LensMakersFormula.html
20cm
To find the focal length of the 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 index of refraction.
- R1 is the radius of curvature of the first surface (outer surface).
- R2 is the radius of curvature of the second surface (inner surface).
Given:
n = 1.5
R1 = 2 cm (convex lens)
R2 = -4 cm (concave lens, negative because the center of curvature is on the opposite side of the lens)
Substituting these values into the formula:
1/f = (1.5 - 1) * (1/2 - 1/-4)
Simplifying:
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
Taking the reciprocal of both sides:
f = 8/3
Therefore, the focal length of the lens is 8/3 cm.
To find the focal length of the lens, we can use the lensmaker's formula, which relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces.
The lensmaker's formula is given as:
1/f = (n - 1) * (1/R1 - 1/R2)
Where:
- f is the focal length of the lens,
- n is the refractive index of the lens material, in this case 1.5,
- R1 is the radius of curvature of the first lens surface, in this case 2 cm,
- R2 is the radius of curvature of the second lens surface, in this case -4 cm (since the concave surface has a negative radius).
Plugging in the values into the formula, we get:
1/f = (1.5 - 1) * (1/2 - 1/(-4))
Simplifying this expression:
1/f = (0.5) * (1/2 + 1/4)
= (0.5) * (2/4 + 1/4)
= (0.5) * (3/4)
= 3/8
Finally, we can find the value of f:
f = 8/3 cm
Therefore, the focal length of the lens is 8/3 cm or approximately 2.67 cm.