1.55 વક્રીભવનાંક ધરાવતા કાચમાંથી બંને સપાટીઓની વક્રતાત્રિજ્યા સમાન હોય તેવા દ્વિ-બહિર્ગોળ લેન્સ બનાવવો છે, તો 20 cm કેન્દ્રલંબાઈ મેળવવા માટે જરૂરી વક્રતાત્રિજ્યા કેટલી હશે ?

A 44 cm
B 2.2 cm
C 22 cm
D 4.4 cm

Verified Solution

Answer & Solution

Correct Answer

(C) 22 cm

Step-by-step Solution

Detailed explanation

C.22 cm
\(f=+20 cm \quad n=1.55\)
\(R _1=+ R \quad R _2=- R\)
લેન્સ મેકરના સૂત્ર પરથી,
\(\frac{1}{f}=(n-1)\left(\frac{1}{ R _1}-\frac{1}{ R _2}\right)\)
\(\therefore \quad \frac{1}{20}=(1.55-1)\left(\frac{1}{R}-\frac{1}{-R}\right)\)
\(\therefore \quad \frac{1}{20}=0.55 \times \frac{2}{R}\)
\(\therefore \quad R =20 \times 0.55 \times 2\)
\(\therefore \quad R =22 cm\)

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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