# Optics: refraction and reflection

• denniszhao
In summary, the problem involves finding incident angles, refraction and reflection angles in a cup filled with a liquid with different refractive indices. The critical angle can be calculated using the equation arcsin (n2/n1), and Snell's law can be used to calculate refraction angles. The diagram needs to be labeled with the appropriate angles and perpendiculars in order to solve for the perpendicular distance y.
denniszhao
Homework Statement
I have no idea how to start with this problem. I am trying to look for all the incident angles, refraction and reflection angles. And i don't know what the two radii are doing with y.
Relevant Equations
critical angle = arcsin (n2/n1)
snell's law for refraction: n1sin(theta1)=n2sin(theta2)
Homework Statement: I have no idea how to start with this problem. I am trying to look for all the incident angles, refraction and reflection angles. And i don't know what the two radii are doing with y.
Homework Equations: critical angle = arcsin (n2/n1)
snell's law for refraction: n1sin(theta1)=n2sin(theta2)

A cup with refractive index n2= 1.8 has outer radius b= 6.0 cm and inner radius a= 4.0 cm. It is filled with a liquid with refractive index n3= 1.3. In the surrounding medium with n1= 1.0, a ray of
light travels along a trajectory that is at a perpendicular distance y from the center of the cup. The ray enters the cup and, reaching the liquid interface at the critical angle, undergoes total internal reflection.

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The first thing to do is to label the diagram with the angles of reflection and refraction. Also draw in the perpendiculars to the surfaces at the points of refraction and reflection (which would both pass through what point?). Once you see what the geometry looks like, you can start with the critical angle and work your through the geometry to get ##y##.

## 1. What is refraction?

Refraction is the bending of light as it passes through different mediums, such as air, water, or glass. This bending occurs because light travels at different speeds in different mediums.

## 2. How does refraction affect the appearance of objects?

Refraction can distort the appearance of objects, making them appear larger, smaller, or even distorted. This is because the light rays are bent as they pass through different mediums, causing the image to be distorted.

## 3. What is the law of refraction?

The law of refraction, also known as Snell's law, describes the relationship between the angle of incidence and the angle of refraction for a light ray passing through different mediums. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two mediums.

## 4. What is total internal reflection?

Total internal reflection occurs when a light ray traveling from a more dense medium to a less dense medium reaches a critical angle and is completely reflected back into the more dense medium. This phenomenon is responsible for the reflective surface of objects such as mirrors and is also used in fiber optics technology.

## 5. How is reflection different from refraction?

Reflection is when light bounces off a surface and changes direction, while refraction is when light passes through a medium and is bent. Reflection occurs at the boundary between two different mediums, while refraction occurs within a single medium.

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