



Reasoning (Key ray rules for a concave lens):
In option (C), the incident ray is aimed towards the lens’s near focus \(F\) (shown by a dashed extension); after refraction it emerges
parallel to the principal axis — exactly matching rule 2. Therefore, (C) is correct.
\[ \text{Concave lens: } \begin{cases} \text{towards } F \;\Rightarrow\; \text{emerges parallel},\\ \text{parallel} \;\Rightarrow\; \text{appears from } F. \end{cases} \]
Why others are wrong (brief): (B) makes a parallel ray pass through the far focus (that’s for a convex lens, not concave). (D) shows parallel rays remaining parallel after the lens (concave lens should diverge them). (A) does not satisfy any standard concave-lens rule as drawn.
Two light beams fall on a transparent material block at point 1 and 2 with angle \( \theta_1 \) and \( \theta_2 \), respectively, as shown in the figure. After refraction, the beams intersect at point 3 which is exactly on the interface at the other end of the block. Given: the distance between 1 and 2, \( d = 4/3 \) cm and \( \theta_1 = \theta_2 = \cos^{-1} \frac{n_2}{2n_1} \), where \( n_2 \) is the refractive index of the block and \( n_1 \) is the refractive index of the outside medium, then the thickness of the block is cm. 
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]