Here are the two questions which appeared in the IIT-JEE 2009 question paper:

(1) A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive ^{–2})

(a) 9 ms^{–1}

(b) 12 ms^{–1}

(c) 16 ms^{–1}

(d) 21.23 ms^{–1}

Even though the real height of of the ball at the instant is *h* (=* *12.8 m), the fish will see the *apparent* height only, which is *μh* where *μ* is the refractive index of water. [Note that the fish is in the denser medium and hence the apparent distance is greater than the real distance.

The real speed of the ball at the height *h* is the speed acquired by its free fall through a distance *x = *20* *– 12.8 = 7.2 m. This speed is √(2*gx*) = √(2×10×7.2) = 12 ms^{–1}.

The *apparent* speed of the ball as seen by the fish is *μ* times the real speed and is equal to (4/3)×12 = 16 ms^{–1}[Option (c)].

(2) A student performed the experiment of determination of focal length of a concave mirror by u–v method using an optical bench of length 1.5 metre. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u, v) values recorded by the student (in cm) are : (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

(a) (42, 56)

(b) (48, 48)

(c) (66, 33)

(d) (78, 39).

This is a very simple question meant for applying the law of distances for a mirror:

1/*v* + 1/*u *= 1/*f*

where *u *is the object distance, *v* is the image distance and *f* is the focal length.

From this *f* = *uv/*(*u+v*)

The sets (a) and (b) give *f = * 24 cm

The set (c) gives *f = *22 cm and the set (d) gives *f = *26 cm

Therefore, the incorrect data sets are (c) and (d).