A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.
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In spherical lenses, the focal length is determined by the radius of curvature of the lens and the refractive index. For a spherical lens, the image is formed by the refraction at both the surfaces of the sphere.
When parallel rays from a distant source fall on a spherical glass ball, they refract at the surface, and the rays converge to form an image. Since the ball is a sphere, the incident rays are refracted at both the entry and exit points, forming a real image on the other side of the ball.
To find the position of the image, we can apply the formula for the refraction at a spherical surface:
\[
\frac{1}{f} = \left( \frac{n - 1}{R} \right)
\]
where:
- \( f \) is the focal length of the spherical ball,
- \( n = 1.5 \) is the refractive index of the glass,
- \( R = 15 \, \text{cm} \) is the radius of the spherical ball.
Substitute the values:
\[
\frac{1}{f} = \frac{1.5 - 1}{15} = \frac{0.5}{15} = \frac{1}{30}
\]
So, the focal length \( f = 30 \, \text{cm} \).
The ray diagram for this setup is shown below:
The image is formed at a distance of 30 cm from the center of the ball. Therefore, the final image is formed 30 cm away from the center on the opposite side of the incident light. Since the source is far away, the rays converge at this point after refracting through the spherical ball.
