Snell’s Law and Total Internal Reflection

 

 

Theoretical Background
When light travels between two different mediums, the velocity and wavelength changes. The
result is the “bending” of the light. The “bending” of light is referred to as refraction. The
“bending” follows a convenient mathematical relationship called Snell’s law, named after Dutch
astronomer Willebrord Snellius (1580-1626). The purpose of this lab is to determine the
relationship between the incident angle of a light beam and the refracted angle of the light beam
as the beam passes from one medium to another. In addition, we will demonstrate an application
of Snell’s Law by measuring the critical angle for a light beam that travels from a more dense
medium to a less dense medium.
Experimental Procedure
Part I: Snell’s Law
1. Watch the Introductory video and follow instructions given. Below I give a step by step
procedure that I use in the video.
2. Open link, this will bring you to a loading screen. Select the ‘More Tools’ icon.
3. Turn on the laser and drag the circular protractor such that the protractor is centered
along the normal line and the boundary between the two mediums. Also, drag the speed
indicator tool out from the tools located at the lower left of the simulation. The laser can
be dragged to change the incident angle. Play with the simulation and try changing some
of the different parameters. Make sure to select “Ray” and check the
“Angles” box.
4. The index of refraction is given by the letter 𝑛𝑛, and is defined as the ration of the speed
of light in a vacuum to the speed of light in the medium, 𝑛𝑛 = 𝑐𝑐
𝑣𝑣
, where 𝑐𝑐 = 3.0 × 108 𝑚𝑚
𝑠𝑠 .
As light travels into different substances the velocity of light decreases. For our purposes
the speed of light in a vacuum will be the same as that of air. Use the speed tool to
measure the velocity of light in the glass. Write the velocity in terms of 𝑐𝑐.
5. Use the definition for the index of refraction to verify that the index of refraction for
glass is 1.5. Show all your work.
6. The relationship between the velocity, frequency, and wavelength of a wave is given by
𝑣𝑣 = 𝜆𝜆𝜆𝜆. Since the frequency remains constant when light travels between different
media, an expression can be written to solve for 𝜆𝜆2.

Sample Solution

Equity imposes upon a Lender a duty to account to the borrower the rents and profits received whilst the Lender is in possession. The purpose of this duty is to discourage wilful default and serves as a safety measure to ensure that the property is being managed with due diligence. The accounts for rents and profits received from the property is limited to the property itself, business, money, security and any other assets that form part of the mortgage property . The mortgagee does not have to account for profits made in the course of business connected to the property.
There are no other duties imposed upon a Lender that safeguards a Borrower’s right of redemption save for the general duty to act in good faith and fairly towards a mortgagor in a Lender’s pursuit to obtain repayment. Lenders often have little or no experience in managing the mortgage property let alone a Borrower’s business. Lenders must simply demonstrate that they were active.
It is recommended that if Lenders are able to take possession, the courts should impose a similar duty on a Lender who seeks to control the mortgage property as a Lender selling a mortgage property: the Lender should take reasonable care to obtain the best rental price for the mortgage property and/or generate profits similar to a reasonable businessman carrying on the same business.
The recommendation would reinforce a mortgagee’s duty to take reasonable care of the property . Reasonable care must be exercised by the mortgagee acting to enforce or safeguard it’s securities, in so much that that mortgagee must not take undue risk when exploiting the mortgage property in pursuit of rents and profits. The account must also include rents and profits the Lender would have received had it not been for their own wilful default or neglect; that is, for everything which he has received, or might or ought to have received, whilst being in possession . The mortgagee will be liable for the rents and profits it ought to have received had it not been for its own wilful default or neglect