CUET · PHYSICS · PYQ PAPER 2023
For an equilateral prism, it is found that angle of minimum deviation is equal to angle of the prism. Find the refractive index of material of the prism.
- A \( \frac{1}{\sqrt{3}} \)
- B \( \sqrt{2} \)
- C \( \frac{1}{\sqrt{2}} \)
- D \( \sqrt{3} \)
Answer & Solution
Correct Answer
(D) \( \sqrt{3} \)
Step-by-step Solution
Detailed explanation
\( A = 60^\circ, \delta_m = 60^\circ \) \( \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin\left(\frac{60^\circ + 60^\circ}{2}\right)}{\sin\left(\frac{60^\circ}{2}\right)} \)…
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Aldehydes and ketones represent two essential classes of organic compounds
which are extensively used in the synthesis of a wide variety of other organic molecules.
Due to the inherent polarity of the central carbonyl group, these substances readily undergo nucleophilic addition reactions.
Broadly speaking, these addition reactions can be categorized into two types:
one in which simple addition of the nucleophilic reagent occurs across the \(> C = O\) bond, and the second type where the initial addition is subsequently followed by the elimination of a water molecule.
A variety of ammonia derivatives, including hydroxylamine, hydrazine, phenylhydrazine,
2, 4-dinitroplhenylhdrazine, and semicarbagide, all belong to this second category of reactions.
These specific derivatives are fundamentally used for the identification and definitive characterization of aldehydes and ketones. Significantly, both types of nucleophilic addition reactions are strongly influenced by both steric and electronic factors.
As a general rule, aliphatic aldehydes exhibit higher reactivity compared to aromatic aldehydes.
The aliphatic aldehydes demonstrate the ability to reduce both Fehling's solution and Tollen's reagent, whereas aromatic aldehydes are limited to reducing only Tollen's reagent.
In a similar manner to aldehydes, aromatic ketones are observed to be less reactive than aliphatic ketones towards all nucleophilic addition reactions.
In a separate context, phenols and carboxylic acids both exhibit acidic properties in nature.
Both classes of compounds readily dissolve in NaOH solution and cause blue litmus to turn red.
However, carboxylic acids stand out as much stronger acids than phenols and thus can decompose sodium bicarbonate \(\left( NaHCO _3\right)\) with the distinct evolution of \(CO _2\) gas, a reaction which phenols do not undergo.
It is important to note that both electron- donating and electron- withdrawing substituents significantly influence the acid strength of both aliphatic as well as aromatic carboxylic acids.
Furthermore, unlike all other common aliphatic acids, formic acid uniquely possesses reducing properties and simultaneously does not display the typical reactions characteristic of the alkyl group.
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