Q100 / 100 · BITSAT 2022 · Physics

An achromatic convergent doublet of two lense in contact has a power of $+5 \mathrm{D}$. The power of converging lens is $+6 \mathrm{D}$. The ratio of the dispersive power of the convergent and divergent lenses is

  • A
    $3: 7$
  • B
    $2: 3$
  • Correct answer
    C
    $1: 5$
  • D
    $5: 3$

Solution

- The condition of achromatism is $W_1 P_1+W_2 P_2=0$ $$ \begin{array}{rlrl} \Rightarrow & W_1 P_1 & =-W_2 P_2 \\ \Rightarrow & & \frac{W_1}{W_2} & =-\frac{P_2}{P_1} \end{array} $$ Now, $\quad P_1+P_2=4 \mathrm{D}$ but, Power of converging lens, $$ P_1=5 \mathrm{D} $$ $\because$ Power of diverging lens $$ \begin{aligned} P_2 & =4 \mathrm{D}-P_1 \\ & =4 \mathrm{D}-5 \mathrm{D}=-\mathrm{D} \end{aligned} $$ [From ii] $\therefore$ From Eq. (i), we have $$ \frac{W_1}{W_2}=-\frac{P_2}{P_1}=\frac{-(-D)}{5 D}=\frac{1}{5} \Rightarrow \frac{W_1}{W_2}=\frac{1}{5} $$

Hence, the correct answer is option: 'C'.

More Ray Optics Questions