Wavelength Conversion in Water: 640 nm Light & Wedge

[lha08]

Homework Statement

Light of wavelength 640 nm in water illuminates a glass (n = 1.5) wedge submerged in water (n = 1.33). If the distance between successive bright fringes is 6 mm.

Homework Equations

The Attempt at a Solution

I have a lot of trouble trying to convert the wavelength of light into the wavelength of water...but the rest i pretty much understand, just that little part that is really frustrating me.

 

[Doc Al]

I have a lot of trouble trying to convert the wavelength of light into the wavelength of water...but the rest i pretty much understand, just that little part that is really frustrating me.

You mean convert the wavelength of light in one medium to the wavelength it would have in another.

It's easiest if you always compare the wavelength in a medium to the wavelength in vacuum (n = 1). λ_n = λ/n. So, 640 nm = λ/1.33. To find the wavelength in glass, you need to figure out λ/1.5.

 

[nlightner]

I understand your frustration with converting the wavelength of light into the wavelength of water. However, it is important to note that the wavelength of light does not change when it enters a different medium such as water. The wavelength of light is a property of the light itself, not the medium it is passing through.

In this scenario, the 640 nm wavelength of light will remain the same when it enters the water and illuminates the glass wedge. The only change that will occur is in the speed at which the light travels, due to the different refractive indices of water and glass.

To calculate the distance between successive bright fringes, we can use the equation d = λL/D, where d is the distance between fringes, λ is the wavelength of light, L is the distance between the light source and the wedge, and D is the distance between the wedge and the screen where the fringes are observed.

In this case, we can substitute the values given in the problem: λ = 640 nm, L = unknown, D = 6 mm. We can solve for L by rearranging the equation to L = dD/λ. Plugging in the values, we get L = (6 mm)(640 nm)/(1.33-1.5) = 0.0096 m.

Therefore, the distance between the light source and the wedge is 0.0096 m or 9.6 mm. I hope this helps with your homework!