30 cm કેન્દ્રલંબાઈના બહિર્ગોળ લેન્સને 10 cm કેન્દ્રલંબાઈના અંતર્ગોળ લેન્સ સાથે સંપર્કમાં રાખ્યો छे. આ સંયોજનની સમતુલ્ય કેન્દ્રલંબાઈ શોધો. (લેન્સની જાડાઈ અવગણો)

A -15 cm
B (-40)CM
C \(-20 cm\)
D \(-30 cm\)

Verified Solution

Answer & Solution

Correct Answer

(A) -15 cm

Step-by-step Solution

Detailed explanation

A.-15cm
બહિર્ગોળ લેન્સની કેન્દ્રલંબાઈ,
\(f_1=+30 cm\)
અંતર્ગોળ લેન્સની કેન્દ્રલંબાઈ,
\(f_2=-10 cm\)
લેન્સના સંયોજનની કેન્દ્રલંબાઈ,
\(\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\)
\(\therefore \quad \frac{1}{f}=\frac{1}{30}+\frac{1}{-10}\)
\(\therefore \quad \frac{1}{f}=\frac{1-3}{30}\)
\(\therefore \quad \frac{1}{f}=\frac{-2}{30}\)
\(\therefore f=-15 cm\)

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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