Physics Assertion (A) & Reason (B) MCQ

2. Both A and R are true but R is not the correct explanation of A.

Explanation:

For an equiconvex lens, R₁ = R₂ = R

From $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$

Using lens maker's formula for glass, $\mu = 1.5$ placed in air $\frac{1}{\text{f}}=(1.5-1)\frac{2}{\text{R}}\Rightarrow\text{f}=\text{R}.$

4. A is false and R is also false.

Explanation:

The distance between the object and its real image is minimum when magnification is I. We know that the magnification of convex lens is given by $\text{m}=-\frac{\text{v}}{\text{u}}$ for m = 1, v = -u.

Now from lens formula, v = u = 2f

Hence, minimum distance v + u = 4f.

1. Both A and R are true and R is the correct explanation of A.

Explanation:

Goggles have zero power.

The focal length is given by $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big).$ For goggle lenses, both sides are curved the same way. R₁ and R₂ are positive. If they are the same, $\frac{1}{\text{f}}=0$ i.e., power is zero.

4. A is false and R is also false.

Explanation:

A convex lens made of glass behaves as a convergent lens when placed in air or water. However when the same lens is immersed in carbon disulphide $(\mu = 1.63),$ it behaves as a divergent lens. Therefore when a convergent lens is placed inside a transparent medium of refractive index greater than that of material of the lens, it behaves as a divergent lens. Behaviour of a lens depends on the refractive index of a surrounding medium.

2. Both A and R are true but R is not the correct explanation of A.

Explanation:

$\mu=\frac{\mu_\text{g}}{\mu_\text{c}}=\frac{1.5}{1.65}<1$

From $\frac{1}{\text{f}}=(\mu-1)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$ f becomes negative.

Therefore, the lens behaves as a diverging lens.

1. Both A and R are true and R is the correct explanation of A.

Explanation:

$\frac{1}{\text{f}}=(^\text{w}\mu_\text{g}-1)\Big[\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big]$

$=\Big(\frac{\mu_\text{g}}{\mu_\text{w}}-{1}\Big)\Big(\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big)$

$\frac{1}{\text{f}}=\Big(\frac{\mu_\text{g}-\mu_\text{w}}{\mu_\text{w}}\Big)\times\Big[\frac{1}{\text{R}_1}-\frac{1}{\text{R}_2}\Big]$

$=\Big(\frac{1.5-1.33}{1.33}\Big)\times\Big[\frac{1}{\text{R}_1}+\frac{1}{\text{R}_2}\Big]$

$\therefore\text{f}=78.24\text{cm}$

2. Both A and R are true but R is not the correct explanation of A.

Explanation:

The light gathering power (or brightness) of a telescope is directly proportional to the area of the objective lens.

i.e., light gathering power $\propto\pi\text{r}^2=\frac{\pi\text{D}^2}{4},$ where D is the diameter of the objective. Thus telescope will have large light gathering power if the diameter of the objective lens is large. So by increasing the objective diameter even far off stars may produce images of optimum brightness.

2. Both A and R are true but R is not the correct explanation of A.

Explanation:

The brilliance of diamond is due to total internal reflection of tight. $\mu$ t for diamond is 2.42, so that critical angle for diamond air interface is C = 24.4° $\big($from sin $\text{C}=\frac{1}{\mu}\big).$ The diamond is cut suitable so that light entering the diamond from any face suffers multiple total internal reflections at the various faces and remains within the diamond Hence the diamond sparkles.

4. A is false and R is also false.

Explanation:

For a prism of small angle A, the angular dispersion produced $=(\mu_\text{v}-\mu_\text{R})\text{A}.$ This can be cancelled by a second prism of angle A' made of different material such that $(\mu'_\text{v}-\mu'_\text{R})\text{A}'=(\mu_\text{v}-\mu_\text{R})\text{A}.$

If only A = A', then the dispersion produced by one prism cannot be cancelled by the dispersion produced by the other prism because,

$(\mu'_\text{v}-\mu'_\text{R})\text{A}'=(\mu_\text{v}-\mu_\text{R})\text{A}$ for different materials Therefore in order to eliminate dispersion by combining two prism they should have same refracting angle and made of same material.