Question Video: Identifying How the Angle of Deviation Varies with the Angle of Incidence for a Triangular Prism | Nagwa Question Video: Identifying How the Angle of Deviation Varies with the Angle of Incidence for a Triangular Prism | Nagwa

Question Video: Identifying How the Angle of Deviation Varies with the Angle of Incidence for a Triangular Prism Physics • Second Year of Secondary School

The graph contains four lines that may or may not correctly represent a plot of how 𝛼, the angle of deviation of the triangular prism shown in the diagram, varies with Φ₁, the angle of incidence of light rays on it. Which of the lines represents the relationship between Φ₁ and 𝛼 correctly?

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Video Transcript

The graph contains four lines that may or may not correctly represent a plot of how 𝛼, the angle of deviation of the triangular prism shown in the diagram, varies with Φ one, the angle of incidence of light rays on it. Which of the lines represents the relationship between Φ one and 𝛼 correctly? (A) Black, (B) blue, (C) green, (D) yellow, (E) red.

In order to answer this question, let’s first recall the equation that relates 𝛼, Φ one, 𝜃 two, and 𝐴. Remember that by using geometric properties of triangles, we can relate the angles of incidence and refraction for a prism. Careful examination of the diagram of rays entering and exiting the prism leads us to this expression: 𝛼 equals Φ one plus 𝜃 two minus 𝐴. We are asked to identify the line on the graph that correctly represents the relationship between Φ one and 𝛼, so let’s look at what kind of graph this expression will create.

We know that 𝐴, the apex angle, is a constant and will not affect the way that Φ one changes with respect to 𝛼. So we can choose to ignore that term. We also know that 𝜃 two is dependent on Φ one. So the only term in the expression that will directly affect 𝛼, the angle of deviation, is Φ one, the angle of incidence. Notice that the graph in our diagram only shows the general shape of a set of curves. To find our answer then, we’ll want to understand roughly how the angle of deviation increases or decreases with respect to the angle of incidence.

The minimum possible angle of deviation happens when the incoming ray passes through the prism exactly parallel to its base. When this happens, Φ one equals 𝜃 two, which means we can write that 𝛼 sub min equals two times Φ one minus 𝐴. Therefore, the minimum angle of deviation occurs at roughly the middle of the range of possible angles of incidence. At other angles of incidence, either lower or higher than this one, the angle of deviation increases. This means we can expect the line to curve upward on both sides of the point we’ve marked out. Overall, the curve will look a bit like a smile.

We can look at the lines given as possible answers and find the one that matches our graph the closest. We can quickly eliminate the yellow and green lines since they are upside down compared to our curve. We can also eliminate the black line since it is a straight line with no curve. We can see further that blue is not the correct answer since it only curves down and does not curve back upward like our line. That leaves us with the correct option: (E) red. The shape of the red line most closely matches the curve that we drew. This shows the correct relationship between Φ one and 𝛼.

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