# Light incident on a sphere, focused at a distance ##2R##

• lorenz0
In summary, focusing light on a sphere at a distance of 2R creates a uniform and concentrated light source, which is useful for scientific experiments and applications. The distance of 2R is significant because it affects the way light interacts with the sphere. Factors such as the power of the light source, distance, material, and angle can influence the intensity of light incident on the sphere. Focusing light at this distance can change the appearance of the sphere, making it brighter, have different colors or sheens, or create shadows. This technique has practical applications in various fields, including optics, astronomy, and photography.
lorenz0
Homework Statement
A solid sphere with index of refraction ##n## and radius ##R##, placed in air, is illuminated by a beam of light coming from a source at a great distance, which is focused on the bottom surface of the sphere. Determine the value of ##n##.
Relevant Equations
##\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}##
I used the equation for the refraction on a spherical surface: ##\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}##, where ##n_1=1## is the index of refraction of air, ##n_2## the index of refraction of the sphere, ##R## is the radius of the glass sphere, ##p## is the object distance which, since the rays are parallel I assumed to be infinite, ##p=\infty##, and ##q## is the image distance, which should be ##q=2R##. Substituting and solving for ##n_2## I get ##n_2=2##.

Does my reasoning make sense? Thanks.

#### Attachments

• refraction.png
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Looks good to me.

Full size image.

## 1. What is the effect of focusing light on a sphere at a distance of 2R?

The light will be concentrated on a smaller area of the sphere, resulting in a brighter and more intense illumination.

## 2. How does the distance of 2R affect the intensity of light incident on a sphere?

The intensity of light will be greatest at the point of focus, but will decrease as the distance from the focus point increases.

## 3. Can the angle of incidence affect the intensity of light on a sphere focused at 2R?

Yes, the angle of incidence can play a role in the intensity of light on the sphere. A steeper angle will result in a more concentrated and intense light, while a shallower angle will result in a more spread out and less intense light.

## 4. How does the curvature of the sphere impact the way light is focused at 2R?

The curvature of the sphere can affect how the light is focused, as it determines the shape of the focal point. A more curved sphere will have a smaller and more intense focal point, while a flatter sphere will have a larger and less intense focal point.

## 5. What other factors can influence the way light is focused on a sphere at 2R?

The refractive index of the material the sphere is made of can also play a role in how light is focused. A higher refractive index will result in a more intense and focused light, while a lower refractive index will result in a less intense and more spread out light. Additionally, the wavelength of the incident light can also impact the way it is focused on the sphere.

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