Refraction due to attractive potential

[missmaria]

Electrons incident on a crystal suffer refraction due to an attractive potential of 15V. If the angle of incidence is 45 degrees and the electrons have an incident energy of 100eV, what is the angle of refraction?

Ok, so i know that i have to use snell's law, but I'm stuck on calculating the effect of the attractive potential of the crystal. please help! thanks

 

[olgranpappy]

Electrons incident on a crystal suffer refraction due to an attractive potential of 15V. If the angle of incidence is 45 degrees and the electrons have an incident energy of 100eV, what is the angle of refraction?

Ok, so i know that i have to use snell's law, but I'm stuck on calculating the effect of the attractive potential of the crystal. please help! thanks

The potential changes the wavelength of the electrons. Thus causing the refraction.

 

[denian]

I would approach this problem by first understanding the concept of refraction and how it is affected by an attractive potential. Refraction is the bending of a wave as it passes through a medium with a different density, and this bending is determined by the angle of incidence and the refractive index of the medium.

In this case, we have an additional factor of the attractive potential of the crystal. This potential will cause the electrons to experience a force towards the crystal, which will affect their trajectory and therefore the angle of refraction.

To calculate the effect of the attractive potential, we can use the concept of potential energy. The potential energy of a charged particle in an electric field is given by the equation PE = qV, where q is the charge of the particle and V is the potential difference. In this case, the potential difference is 15V.

Therefore, the potential energy of the electrons incident on the crystal will be 100eV x 15V = 1500eV. This additional potential energy will cause the electrons to deviate from their original path and will result in a change in the angle of refraction.

To determine the angle of refraction, we can use Snell's law which 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 refractive indices of the two media.

In this case, the angle of incidence is given as 45 degrees, and we know the refractive index of the medium (crystal) is affected by the attractive potential. Therefore, we can write the equation as sin 45 degrees / sin θ = 1 / n, where θ is the angle of refraction and n is the effective refractive index of the crystal.

To solve for θ, we need to determine the value of n. This can be done by considering the potential energy of the electrons and using the equation for potential energy to determine the effective refractive index.

Once we have determined the value of n, we can solve for θ using the equation above. This will give us the angle of refraction for the electrons incident on the crystal with an incident energy of 100eV and an angle of incidence of 45 degrees.

In summary, the angle of refraction in this scenario can be calculated by taking into account the attractive potential of the crystal and using Snell's law to determine the effective refractive index. This