Prisim and angle of deviation problem

[buttterfly41]

Light of wavelength 700 nm is incident on the face of a fused quartz prism at an angle of 77.0° (with respect to the normal to the surface). The apex angle of the prism is 60.0°. n=1.459.

a) the angle of refraction at the first surface
(b) the angle of incidence at the second surface
(c) the angle of refraction at the second surface
(d) the angle between the incident and emerging rays

i understand the first three by using geometry and snells law.. answers fro a) 41.9, for b) 18.1, for c)27.0. But i do not understand how to obtain the answer for part d. I thought it was asking for the angle of deviation in essence i thought , which is abs(theata1 - theata2). but other than that guess i don't know where else to take it from.

Any help would be wonderful. thankyou.

 

[Kurdt]

Try drawing a diagram of the ray path and it will help you see how to get the angle.

 

[m2003]

Dear reader,

Thank you for your question. I would like to provide you with a comprehensive response to your query.

Firstly, let's review the given information. We have a fused quartz prism with an apex angle of 60.0° and an incident light of wavelength 700 nm at an angle of 77.0° with respect to the normal to the surface. The refractive index of the prism is given as 1.459.

Using Snell's law, we can calculate the angle of refraction at the first surface (a) as 41.9°, the angle of incidence at the second surface (b) as 18.1°, and the angle of refraction at the second surface (c) as 27.0°. These values can be obtained using the formula n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the initial and final mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively.

Now, let's move on to the fourth part of the problem, which asks for the angle between the incident and emerging rays (d). This angle is also known as the angle of deviation. In order to calculate this value, we need to use the prism equation, which is given as:

A + δ = (n - 1)(A - ε)

Where A is the apex angle of the prism, δ is the angle of deviation, n is the refractive index of the prism, and ε is the angle of minimum deviation.

We know that A = 60.0° and n = 1.459. To find the angle of minimum deviation (ε), we can use the formula ε = (A/2)(n - 1). Plugging in the values, we get ε = (60.0/2)(1.459 - 1) = 14.775°.

Substituting the values of A, n, and ε in the prism equation, we get:

60.0 + δ = (1.459 - 1)(60.0 - 14.775)
δ = 27.225°

Therefore, the angle between the incident and emerging rays (d) is 27.225°.

To summarize, the answers for the given problem are:

a) the angle of refraction at the first surface = 41