Posted: September 18th, 2022

# Question

Lab9-Optics2 x

Reflection from Plane Mirror and Curved Mirror, and Snell’s Law

Part I: Snell’s Law:
When a light ray passes through an interface between two materials with different indices of refraction, the light ray direction changes according to Snell’s Law. The incoming light ray is termed the incident ray and the bent ray which is transmitted through the interface is called the refracted ray. The law states:

𝑛𝑖 sin(𝜃𝑖) = 𝑛𝑟 sin(𝜃𝑟) (1)

## FIGURE 1. Snell’s law

LAB

9

Here, the subscript i indicates incident and r indicates refracted. We can solve for the following relation:

Sin θi = (nr/ni) Sin θr (2)

So if we plot sin(i) on the vertical axis and sin(r) on the horizontal, we should get a straight line with slope equal to nr/ni, the ratio of the refractive indices.

This lab is designed to have students investigate the relationship between the angle of incidence and refraction between two medium and test Snell’s law. You will measure the angle of incidence and refraction for four different cases. For each case you will follow the same procedure to record data. You will also see the phenomenon of total internal reflection.

## OBJECTIVES

· Determine the relationship between incident and refracted angles.

· Compare simulated refraction with theoretical formula.

· Observe phenomenon of total internal reflection.

· Determine angle of internal reflection for

glass

/

water

interface.

· Make images with plane mirror and curved mirrors.

## INITIAL SETUP

Follow this link and open simulation lab:

You should see the screen shown in Figure 2.

## FIGURE 2: the simulation

FIGURE 3: How to measure the angles.

## PROCEDURE:

This protocol will generate data that you will be able to analyze. Do this protocol for each type of interface (the types of interface are listed in Table 1).

1. First choose the upper and lower material using the controls on the right.

2. Now, place the protractor to measure the angles as shown in Figure 1.

3. Now adjust the position of the laser to an angle of incidence.

4. Record the values of the angle of incidence and the angle of refraction in a table.

5. Repeat for angle of incidence from 0 to 90 in steps of 10 degrees.

Snell’s Law

Repeat this protocol for four interfaces:

## TABLE 1: the types of interfaces

air

water

glass

glass

water

 Interface Upper material Lower material 1 air water 2 glass 3 4

ANALYSIS

So there will be 4 data sets. For each data set follow the analysis steps:

1. enter all data into excel

2. create a graph of angle of incidence on horizontal axis and angle of refraction on vertical. Label all axes. Include in report.

3. Now transform the data to create two new columns containing the sine of the angles.

4. create a new plot of sin(i) on the vertical axis and sin(r) on the horizontal. (Note this is flipping the horizontal and vertical axis from step 2.)

5. Add a linear trend line. Include graph of transformed data with linear fit with equation in your report.

6. Record the slope of the line from step 5 to the data table and consider it as experimental value of nr/ni.

7. Determine the theoretical slope or theoretical value of nr/ni from the simulation page. Record it on the table.

8. Find percent error between theoretical and experimental value of nr/ni.

© 2021 taken from PHET, modified by Dr Dipti Sharma

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