Light rays from a source are incident on a glass prism of index of refraction μ and angle of prism α. At near normal incidence, the angle of deviation of the emerging rays is
Variation of angle of deviation δ versus angle of incidence for a prism is given the figure. The value of refractive index of prism :
In the displacement method, a convex lens is placed in between an object and a screen. If magnification in the two positions are \(m_1\) and \(m_2\) (\(m_1 > m_2\)) and the distance between two positions of the lens is x, the focal length of the lens is
In displacement method, \(m_1 = \frac{v_1}{u_1}\) and \(m_2 = \frac{v_2}{u_2} = \frac{u_1}{v_1}\). Since the distance between two positions is \(x = v_1 - u_1\), we obtain \(m_1 - m_2 = \frac{x}{f}\), hence \(f = \frac{x}{m_1-m_2}\).
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The mass density of an optically denser medium is greater than that of an optically rarer medium.
Reason R: Optical density is found by the ratio of the speed of light in two media while mass density is mass per unit volume.
In the light of the above statements, choose the correct answer from the option given below.
Mass density and optical density are not directly related. For example, oil is optically denser than water but has a lower mass density. Thus, Assertion A is false but Reason R is true.
If a container of height \(17.3\text{ cm}\) is filled with a liquid of refractive index \(\mu\). The bottom of container appear to be raised by \(3.46\text{ cm}\) when seen from above. Refractive index of liquid is
The apparent shift is \(s = d\left(1 - \frac{1}{\mu}\right)\). Substituting the values: \(3.46 = 17.3 \left(1 - \frac{1}{\mu}\right) \implies 1 - \frac{1}{\mu} = 0.2 \implies \mu = 1.25\).
The refracting angle and minimum angle of deviation of a prism is same as \(60^\circ\). The refractive index of prism is
Using the prism formula: \(\mu = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin(A/2)}\). Since \(A = D_m = 60^\circ\), \(\mu = \frac{\sin(60^\circ)}{\sin(30^\circ)} = \sqrt{3} \approx 1.732\).
Match the elements of List-I with List-II:
A simple microscope forms an erect, virtual, and enlarged image (A-H). A compound microscope forms a magnified, inverted, and virtual final image (B-E). An astronomical telescope has a virtual, inverted, high resolution final image (C-G). A terrestrial telescope has a virtual, erect, high resolution final image (D-F).