A parallel beam of light enters a clear plastic bead 2.50cm in diameter and refractive index 1.44 .the point beyond the bead are these rays brought to focus is
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0.795cm
To find the point where the rays are brought to focus, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance
u = object distance
In this case, the clear plastic bead is acting as a lens. The refractive index of the lens, μ = 1.44.
The diameter of the bead, d = 2.50 cm. The radius, r = d/2 = 1.25 cm = 0.0125 m.
Since the light enters the bead parallel to the principal axis, the object distance (u) is infinity (∞).
The focal length (f) of a lens can be calculated using the formula:
f = (μ - 1) * R
Where:
R = radius of curvature of the lens
Since the bead is spherical, the radius of curvature (R) is equal to twice the radius (2 * r).
R = 2 * r = 2 * 0.0125 m = 0.025 m
Now, substitute the values into the formula to find the focal length:
f = (1.44 - 1) * 0.025 m = 0.036 m
Now, plug the values of u and f into the lens formula and solve for v:
1/f = 1/v - 1/u
Since u = ∞, 1/u = 0. Therefore:
1/f = 1/v
v = f = 0.036 m
So, the rays are brought to focus at a point 0.036 m (or 3.6 cm) beyond the bead.