Final answer:
Consider a plane wave incident on a convex lens of diameter 5cm and of focal length 10 cm, the radius of the first dark ring on the focal plane of a convex lens is 0.06cm
Step-by-step explanation:
To calculate the radius of the first dark ring on the focal plane of a convex lens, we can use the formula for the radius of the nth dark ring:
rn = sqrt((n * λ * f * D) / (D + n * λ))
Where:
rn is the radius of the nth dark ring
n is the number of the dark ring (1 for the first dark ring)
λ is the wavelength of the incident light
f is the focal length of the lens
D is the diameter of the lens
Let's calculate the radius of the first dark ring for a lens with a diameter of 5cm and a focal length of 10cm:
r1 = sqrt((1 * 6000A * 10cm * 5cm) / (5cm + 1 * 6000A))
r1 = 0.03cm
For a lens with a diameter of 15cm and a focal length of 10cm:
r1 = sqrt((1 * 6000A * 10cm * 15cm) / (15cm + 1 * 6000A))
r1 = 0.06cm
The physical interpretation of these results is that the first dark ring on the focal plane of the lens represents the destructive interference between the incident rays of light, resulting in a decrease in intensity in that region.
So therefore the radius of the first dark ring on the focal plane of a convex lens is 0.06cm