Question
An achromatic convergent doublet of two lense in contact has a power of +5 D . The power of converging lens is +6 D . The ratio of the dispersive power of the convergent and divergent lenses is
BITSAT
Physics
Ray Optics
2022
BITSAT 2022
BITSAT Physics Question (2022) — Solution
Options
- A. 3: 7
- B. 2: 3
- C. 1: 5
- D. 5: 3
Answer
C. 1: 5
Step-by-step solution
- The condition of achromatism is W_1 P_1+W_2 P_2=0 array rlrl & W_1 P_1 & =-W_2 P_2 \\ & & W_1 W_2 & =- P_2 P_1 array Now, P_1+P_2=4 D but, Power of converging lens, P_1=5 D Power of diverging lens aligned P_2 & =4 D -P_1 \\ & =4 D -5 D =- D aligned [From ii] From Eq. (i), we have W_1 W_2 =- P_2 P_1 = -(-D) 5 D = 1 5 W_1 W_2 = 1 5
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