Step 1: Relation in Prism
From the prism relation:
$$ r_1 + c = A $$
Rearranging for \( r_1 \):
$$ r_1 = 90^\circ - c \quad \text{...(1)} $$
Step 2: Expression for \( \cos c \)
We know:
$$ \sin c = \frac{1}{\mu} $$
Using trigonometric identity:
$$ \cos c = \frac{\sqrt{\mu^2 - 1}}{\mu} $$
Step 3: Apply Snell's Law on Incidence Surface
Using Snell’s law at the first surface:
$$ \sin 30^\circ = \mu \sin (r_1) $$
Substituting \( r_1 = 90^\circ - c \):
$$ \frac{1}{2} = \mu \sin (90^\circ - c) $$
Since \( \sin (90^\circ - c) = \cos c \), we get:
$$ \frac{1}{2} = \mu \times \frac{\sqrt{\mu^2 - 1}}{\mu} $$
Simplifying:
$$ \frac{1}{2} = \frac{\sqrt{\mu^2 - 1}}{1} $$
Step 4: Solve for \( \mu \)
Squaring both sides:
$$ \frac{1}{4} = \mu^2 - 1 $$
Rearranging:
$$ \mu^2 = \frac{5}{4} $$
Taking square root:
$$ \mu = \frac{\sqrt{5}}{2} $$
Conclusion
The refractive index \( \mu \) of the prism is \(\frac{\sqrt{5}}{2}\).
What is atomic model of magnetism? Differentiate between paramagnetic, diamagnetic, and ferromagnetic substances on this basis. Also, give one example of each.
The following diagram shown restriction sites in E. coli cloning vector pBR322. Find the role of ‘X’ and ‘Y’gens :