A convex lens and a concave lens, each having the same focal length of 25 cm, are put in contact to form a combination of lenses. The power in dioptres of the combination is :

1. 25

2. 50

3. infinite

4. zero

Pick the wrong statement in the context with a rainbow.

1. Rainbow is a combined effect of dispersion, refraction, and reflection of sunlight.

2. When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed.

3.  The order of colors is reversed in the secondary rainbow.

4. An observer can see a rainbow when his front is towards the sun.

Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerin which has the same refractive index ($\mu =1.5$) as that of glass, then the equivalent focal length is $F_2$. The ratio $F_1:F_2$ will be:

1. 3 : 4

2. 2 : 1

3. 1 : 2

4. 2 : 3

A ray of light falls on a plane mirror A kept at an angle 90$°$ to mirror B as shown in the figure. The angle N is :

1.  30$°$

2.  45$°$

3.  60$°$

4.  90$°$

Which of the following ray diagrams is correct?

1.  

2.  

3.  

4.  

A concave lens gives a virtual image. In optical lenses worn by humans which of the following statements is true?

1.  The lens can never be concave.

2.  In some cases, the lens can be concave if the focal length is much larger than 2.5 cm.

3.  All focal length concave lenses are possible.

4.  All focal length Convex lenses are possible.

A ray of light in air is incident on an equilateral glass prism at an angle ${\theta }_i$ to the normal. After refraction, the light traveled parallel to the base of prism and emerged in the air at an angle ${\theta }_0$ to the normal. If the angle between the incident and the emergent rays is 60$°$ then the refractive index of glass with respect to air is :

1. 1.33

2. 1.5

3. 1.73

4. 1.66

You are standing on the shore of a lake. You spot a fish swimming below the lake surface. You want to kill the fish first by throwing a spear and next, by pointing a high-power laser torch. How should you aim the spear and torch, respectively, from the options given below?

I. above the apparent position of the fish
II.  below the apparent position of the fish
III. directly at the apparent position of the fish

1. SPEAR: II        : LASER: III

2. SPEAR: I        : LASER: II

3. SPEAR: II       : LASER: II

4. SPEAR: III      : LASER: III

A beam of light coming from a rarer medium is partially reflected from the surface of a denser medium and partially refracted into the denser medium. If the reflected and the refracted rays are perpendicular to each other and the ratio of the refractive indices of the denser and rarer medium is $\sqrt{3}$ , the angle of refraction will be -

1. $60°$

2. $30°$

3. $45°$

4. $41.5°$

A person can see clearly only the objects situated in the range of 50 cm to 300 cm. He went to an optometrist who prescribed him a lens of a certain power to increase the maximum distance of his vision to infinity, i.e., it corrected the nearsightedness. However, upon using the prescribed lens the person discovered that the near point of his vision has shifted from 50 cm to a distance "d". What is the value of d?

1. 60 cm

2. 100 cm

3. 40 cm

4. 500 cm