હવામાં રાખેલા એક બિંદુવત્ ઉદ્ગમમાંથી પ્રકાશ એક કાચની ગોળીય સપાટી (n = 1.5 અને વક્રતાત્રિજ્યા = 20 cm) પર આપાત થાય છે. આ ગોળીય સપાટીથી પ્રકાશ ઉદ્ગમ 100 cm દૂર છે. પ્રતિબિંબ કયા સ્થાને રચાશે.

A -100 cm
B -200 cm
C 200 cm
D 100 cm

Verified Solution

Answer & Solution

Correct Answer

(D) 100 cm

Step-by-step Solution

Detailed explanation

D.100 cm
\(R =+20 cm\)
\(n_1=1 \quad n_2=1.5\)
\(u=-100 cm \quad v=?\)}
\(\frac{n_2}{u}-\frac{n_1}{u}=\frac{n_2-n_1}{ R }\)
\(\therefore \frac{1.5}{v}-\frac{1}{-100}=\frac{1.5-1}{20}\)
\(\therefore \quad \frac{1.5}{v}+\frac{1}{100}=\frac{0.5}{20}\)
\(\therefore \quad \frac{1.5}{v}=\frac{0.5}{20}-\frac{1}{100}\)
\(\therefore \quad \frac{1.5}{v}=\frac{2.5-1}{100}\)
\(\therefore \quad \frac{1.5}{v}=\frac{1.5}{100}\)
\(\therefore \quad v=+100 cm\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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