Prisms and Dispersion: NEET Problem Solving

1. Problems on Minimum Deviation

The condition of minimum deviation is a favorite for examiners because of its unique properties: the angle of incidence equals the angle of emergence ($i=e$), the internal refracted ray is parallel to the prism's base, and the two internal angles are equal ($r_1=r_2=A/2$).

Let's watch a segment where these concepts are used to solve a few typical exam questions.

The key strategies you saw were:

• For minimum deviation, you can immediately set $i_1=i_2$ and $r_1=r_2=A/2$.
• The general deviation formula $\delta =i_1+i_2-A$ simplifies to ${\delta }_m=2i_1-A$, which is often a faster way to find $i_1$ or ${\delta }_m$ than using the full prism formula.
• You can always fall back on applying Snell's Law at the first surface: $1\cdot \sin i_1=\mu \cdot \sin r_1$.

2. Problems on Thin Prisms and Dispersion

For thin prisms ($A\le 10^{\circ }$), the small angle approximation simplifies our calculations significantly. The formula $\delta =(\mu -1)A$ is the starting point for all problems in this category.

Let's watch two worked examples, one of which involves a common variation: placing a mirror after the prism.

The mirror problem highlights an important skill: breaking a complex problem into sequential steps. The total deviation is the sum of deviations from each optical element the ray encounters.

Now, let's revisit dispersive power with a problem that requires the approximation for the mean refractive index, ${\mu }_y$, which we discussed in the last lesson.

3. Combination of Prisms

A more advanced set of problems involves combining two prisms (usually made of different materials like crown and flint glass) to achieve a specific outcome. The prisms are typically placed with their refracting angles oriented oppositely.

There are two primary configurations you must master:

Case 1: Deviation without Dispersion (Achromatic Combination)
The goal is to bend a beam of white light without splitting it into colors. The emergent ray is white and deviated.

• Condition: The net angular dispersion is zero. ${\theta }_{net}={\theta }_1-{\theta }_2=0$.
• Formula: $({\mu }_{v1}-{\mu }_{r1})A_1=({\mu }_{v2}-{\mu }_{r2})A_2$
• Net Deviation: ${\delta }_{net}={\delta }_{y1}-{\delta }_{y2}=({\mu }_{y1}-1)A_1-({\mu }_{y2}-1)A_2$

Case 2: Dispersion without Deviation (Direct-Vision Spectroscope)
The goal is to split white light into a spectrum, but have the mean (yellow) ray emerge parallel to the incident direction.

• Condition: The net deviation of the mean ray is zero. ${\delta }_{net}={\delta }_{y1}-{\delta }_{y2}=0$.
• Formula: $({\mu }_{y1}-1)A_1=({\mu }_{y2}-1)A_2$
• Net Dispersion: ${\theta }_{net}={\theta }_1-{\theta }_2=({\mu }_{v1}-{\mu }_{r1})A_1-({\mu }_{v2}-{\mu }_{r2})A_2$

Let's see an example of Case 1 (Achromatic Combination) being solved.

4. NEET Practice Drill

Now it's your turn. The following resource contains a large bank of NEET-style questions. I have selected a few that cover the concepts we've discussed. Try to solve them on your own before looking up the answers.

Conclusion

Excellent work today. We've methodically applied our entire prism toolkit to a range of NEET-style problems. The key to success is not just knowing the formulas, but recognizing which one to apply based on the problem's conditions.

Key Takeaways:

• Always identify the type of problem first: minimum deviation, thin prism, or a combination.
• For minimum deviation, use the special conditions ($i=e$, $r_1=r_2$) to simplify the problem.
• For combinations of prisms, the key is to correctly set up the condition: either net dispersion is zero (${\theta }_{net}=0$) or net deviation is zero (${\delta }_{net}=0$).
• Don't be afraid to break complex problems (like those with mirrors) into a sequence of simpler steps.

Preview of the Next Lesson:
We have now completed our study of prisms. In the next module, we will move on to the next major topic in Ray Optics: Thin Lenses. We will start by learning how to construct ray diagrams for convex and concave lenses to determine image characteristics, which aligns perfectly with your preference for mastering visual representations before tackling the mathematics.