2 Light Questions?

Question

I need help on this matter, so please tell me which forumlae to use and how you solved them, thanks.

1)A light ray in air strikes a piece of glass with an incident angle of 40 degrees. What is the angle of refraction if the refractive index of glass is 1.45?

2)A beam of red light (A = 650 x 10^-9m) strikes a double slit appartus. The seperation of the slits is 5.00 x 10^-6m. The resulting interference pattern is viewed on a screen 2m away. How far from the central maximum is the first bright spot?

Answer 1

1) Snell's law. The ratio of the angle of incidence (measured from the normal) to the initial index (air) is equal to the ratio of the angle of refraction (likewise measured from the normal) to the final index (glass). Air has an index of refraction of about 1. Use that to solve for the refraction angle.



2) It's all about path length difference. Try to write an expression for the path length from the slit to an arbitrary point on the screen. When the path length difference is a multiple of the wavelength, you'll get a bright spot. When it is an odd-half multiple, you'll get a dark spot. If you want more detailed help with the formulae, look up "Young's experiment" in wikipedia.

Answer 2

These are both pretty simple plug & chug optics problems; it's just a matter of knowing the proper formulas.



1) For this problem, refer to Snell's law :



N_1 * sin(theta_1) = N_2 * sin(theta_2)



where the N's are the refractive indices for the media, theta_1 is the angle of incidence, and theta_2 is the angle of refraction. The N-value for air is approximately the N-value for a vacuum (i.e. 1), so you can work backwards from the data and find that:



angle of refraction = theta_2 = arcsin ( sin(theta_1)/ N_2 )





2) This also has a simple formula solution. The formula can be demonstrated geometrically & I've linked to a page that does demonstrate it, but if you're just looking for a solution:



lamda = w*s/ D



where lamda is the wavelength of light involved, s is the slit separation, D is the distance from the slits to the screen, and w is the fringe separation (which is what you're looking for. Doing a little algebraic rearranging:



w = lamda*D / s.

Answer 3

sin(angle1)/sin(angle2)=n. Therefore, sin(angle2)=sin(angle1)/n.

You have angle1 and n. Solve.



Delta-x=LA/d (using your symbol A for lambda, the wavelength).

Delta-x is the separation between nodal lines, which equals the separation between bright spots. The centre is bright. So the next bright spot is Delta-x away.

Answer 4

This looks like homework. We would need to know where you are stuck.