3) Find out the Focal length for the following lenses (in all cases, the lens is made of a glass with index of 1.5):
a) Bi-convex lens with R, v 30cm.V R, V 20cm,
b) Planar-concave lens with radius of Rv 50cm,
c) Meniscus convex lens with R v 30cm, R, V 20cm.
I need this answer in like 30 minutes if possible, thank u so much!
To find the focal length of a lens, we need to use the lens formula:
1/f = (n - 1) * ((1/R1) - (1/R2))
Where:
f = focal length
n = refractive index of the lens material (given as 1.5 in this case)
R1 and R2 = radii of curvature of the lens surfaces
Let's go through each lens one by one:
a) Bi-convex lens with R1 = Rv = 30cm, R2 = Rv = 20cm:
1/f = (1.5 - 1) * ((1/30) - (1/20))
1/f = 0.5 * ((20/600) - (30/600))
1/f = 0.5 * (-10/600)
1/f = -0.00833 (approximately)
Therefore, the focal length of the bi-convex lens is approximately -120cm (since 1/f = -0.00833 implies f = -1/-0.00833 = 120cm)
b) Planar-concave lens with Rv = 50cm:
Since it is a planar-concave lens, one side is flat (R1 = infinity) and the other side has R2 = Rv = 50cm.
1/f = (1.5 - 1) * ((1/infinity) - (1/50))
(Note: 1/infinity is taken as 0)
1/f = 0.5 * (0 - (1/50))
1/f = 0.5 * (-1/50)
1/f = -0.01 (approximately)
Therefore, the focal length of the planar-concave lens is approximately -100cm.
c) Meniscus convex lens with R1 = Rv = 30cm, R2 = Rv = 20cm:
1/f = (1.5 - 1) * ((1/30) - (1/20))
1/f = 0.5 * ((20/600) - (30/600))
1/f = 0.5 * (-10/600)
1/f = -0.00833 (approximately)
Therefore, the focal length of the meniscus convex lens is approximately -120cm.
Please note that the negative sign indicates that the lens is a diverging lens and the focal length is on the opposite side of the incident light.