Answer : Option C

Explanation :

The focal length of the combination is given by

           `1/F = 1/f_1 + 1/f_2`

Here :  F = 80 cm = 0.8 m.,  `f_1` = 20 cm  = 0.2 m.

`:.`       `1/f_2` =` 1/F - 1/f_1`

or       `1/f_2 `= `1/0.8 - 1/0.2`

or       `1/f_2` = `(1 - 4)/(0.8) = -3/0.8 =  - 3.75`

But   `   p = 1/f`

So, power  `p_2 = 1/f_2`

Hence , `p_2` = - 3.75 D

Answer : Option B

Explanation :

From the relation , `mu = 1/sin C`

or   ` c_v/c_m = 1/sinC`

where C = critical angle = `30^circ`

`c_v` = velocity of light in vacuum  = 3 x `10^8` m/s

`c_m` = velocity of light in medium

Therefore ,  `(3 xx 10^8)/(c_m) = (1)/(sin30^circ)`

or  `c_m= 1/2 xx 3 xx 10^8`

               = 1.5 x` 10^8` m/s

Answer : Option D

Explanation :

For small angled prism -   `delta m = (mu - 1)A`

where  `delta m ` = deviation of light in prism,

`mu` = refractive index = 1.5

A = angle of prism = `6^circ`

Therefore , `delta m` = (1.5 - 1) x `6^circ`

                                  = 0.5 x `6^circ =   3^circ`  

Answer : Option D

Explanation :

Number of images = `(360^circ)/(theta)-1`

                               = `(360^circ)/(45^circ) - 1`

                                = 8 - 1 = 7

Answer : Option A

Explanation :

According to the first law of thermodynamics

                    `Delta Q = Delta W + Delta u`

Given :         `Delta Q = 2 xx 10^3 xx 4.2 J`

                     `Delta W =  500 J`

So,               ` Delta u = 2 xx 10^3 xx 4.2 J - 500 J`

                      `            = 8400 - 500 =   7900 J`