The convex meniscus lens has a 15cm radius for the convex surface and 20cm for the concave surface. The lens is made of crown glass with refractive index, n=1.52 and is surrounded by air.
What is the focal length of the lens.
Aren't there standard formulas for all this?
To find the focal length of the lens, we can use the lensmaker's formula, which states:
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 (crown glass in this case, with n = 1.52)
- R1 is the radius of curvature of the convex surface
- R2 is the radius of curvature of the concave surface
Given that the radius of the convex surface is 15 cm and the radius of the concave surface is 20 cm, we can substitute these values into the lensmaker's formula:
1/f = (1.52 - 1) * ((1/15) - (1/20))
Simplifying further:
1/f = 0.52 * ((20 - 15) / (300))
1/f = 0.52 * (5 / 300)
1/f = 0.00867
Finally, we can find the focal length by taking the reciprocal of both sides:
f = 1 / 0.00867
f ≈ 115.1 cm
Therefore, the focal length of the lens is approximately 115.1 cm.
To calculate the focal length of the lens, we can use the lens maker's formula which relates the focal length (f) of a lens to its radii of curvature (R1 and R2) and the refractive index (n) of the lens material.
The lens maker's formula is given by:
1/f = (n - 1) * ((1/R1) - (1/R2))
Given:
R1 = 15 cm (radius of the convex surface)
R2 = -20 cm (negative sign indicates concave surface)
n = 1.52 (refractive index of crown glass)
Substituting these values into the formula, we get:
1/f = (1.52 - 1) * ((1/15) - (1/(-20)))
Now, let's simplify this expression:
1/f = 0.52 * (1/15 + 1/20)
To add the fractions, we need a common denominator:
1/f = 0.52 * (4/60 + 3/60)
= 0.52 * (7/60)
= 0.52 * (7/60)
= 0.03613
Now, let's find the reciprocal to get the focal length:
f = 1 / 0.03613
≈ 27.69 cm
Therefore, the focal length of the lens is approximately 27.69 cm.