Assertion (A): It is never possible to produce a real image using a plane mirror.
Reason (R): Radius of curvature of a plane mirror is negative.
Assertion (A) is true as plane mirrors always form virtual images.
Reason (R) is false because the radius of curvature of a plane mirror is infinite.
Therefore, (A) is true and (R) is false.
Assertion (A): A dentist uses a concave mirror to examine a small cavity.
Reason (R): A concave mirror always forms a magnified and erect image.
Assertion (A) is true; dentists use concave mirrors for magnified virtual images.
Reason (R) is false as a concave mirror forms magnified and erect images only when the object is between the pole and focal point. It can also form real and inverted images.
Thus, (A) is true and (R) is false.
Assertion (A): Law of reflection is applicable for all type of mirrors.
Reason (R): Rays which are parallel to the principal axis are known as paraxial rays.
Assertion (A) is true. The laws of reflection hold for all types of mirrors.
Reason (R) is false. Paraxial rays are rays close to and making small angles with the principal axis; not all parallel rays are paraxial, nor are all paraxial rays parallel to the axis.
Hence, (A) is true and (R) is false.
Assertion (A): Minimum distance between a real object and its real image formed by a convex lens is three times the focal length of lens.
Reason (R): Distance between an object and its real image formed by convex lens is minimum when magnification produced by the lens has minimum value.
For a convex lens, the minimum distance between a real object and its real image is \(4f\), occurring when the object is placed at \(2f\). At this point, the magnification is \(|m|=1\). The minimum magnitude of magnification approaches zero as the object moves to infinity. Hence, both Assertion (A) and Reason (R) are false.
Assertion (A): A concave mirror and a concave lens have the same focal length in air. When dipped in water, the focal length of the two are equal.
Reason (R): The focal length depends only on the radii of curvature.
The focal length of a mirror \(f_m = R/2\) depends only on its radius of curvature and is independent of the surrounding medium. The focal length of a lens \(1/f_l = (n_l/n_m - 1)(1/R_1 - 1/R_2)\) depends on the refractive indices of the lens material (\(n_l\)) and the surrounding medium (\(n_m\)), as well as radii of curvature. Thus, Assertion (A) is false as their focal lengths are generally not equal and lens focal length changes with medium. Reason (R) is false as lens focal length also depends on refractive indices.
Assertion (A): Light of wavelength \(5500 \text A^0\) travelling in medium 1 is incident on an interface and gets refracted into medium 2. Due to refraction, if it deviates by an angle \(15^{\circ}\), then its wavelength in medium 2 could be greater than or smaller than \(5500 \text{ A^0}\) but never the same.
Reason (R): As light is refracted, its colour changes.
During refraction, the frequency of light remains constant, which means its color does not change. However, its wavelength \(\lambda\) and speed \(v\) change such that \(n_1\lambda_1 = n_2\lambda_2\). Since the light deviates, \(n_1 \neq n_2\), implying \(\lambda_1 \neq \lambda_2\). Thus, Assertion (A) is true and Reason (R) is false.
Assertion (A): If an air bubble is trapped in a glass slab will not produce any lens action.
Reason (R): Behaviour of a shape like a lens is in dependent of surrounding medium.
An air bubble in a glass slab (\(n_{\text{air}} < n_{\text{glass}}\)) acts as a diverging lens, thus producing lens action. So, Assertion (A) is false. Assuming 'in dependent' is a typo for 'independent', Reason (R) 'Behaviour of a shape like a lens is independent of surrounding medium' would also be false, as lens focal length (and hence behavior) is highly dependent on the surrounding medium. Therefore, both A and R are false under this interpretation.
Assertion (A): A prism of refracting angle \(60^{\circ}\) is made of a material of refractive index \(\sqrt{2}\) for a certain wavelength. As light of this wavelength passes through the prism, the prism, angle of minimum deviation is \(30^{\circ}\).
Reason (R): At minimum deviation, angle of refraction of the first face is \(r_1 = A/2 = 30^{\circ}\).
For a prism at minimum deviation, the angle of refraction at the first face is \(r_1 = A/2\), where \(A\) is the prism angle. Given \(A = 60^{\circ}\), \(r_1 = 30^{\circ}\). This makes Reason (R) true. Using the prism formula \(n = \frac{sin((A + \delta_m)/2)}{sin(A/2)}\), with \(n=\sqrt{2}\) and \(A=60^{\circ}\), we find \(\delta_m = 30^{\circ}\). Thus, Assertion (A) is also true. Reason (R) provides a key condition used in calculating the minimum deviation, hence it is the correct explanation for (A).
Assertion (A): When a glass prism is immersed in water, the deviation caused by prism decrease.
Reason (R): Refractive index of glass prism relative to water is less than relative to air.
Deviation is given by (delta = (mu-1)A), where (mu), is the relative refractive index. When immersed in water, (mu_{gw} = mu_g/mu_w), which is less than (mu_{ga} = mu_g), (refractive index w.r.t. air). A smaller (mu), leads to a smaller deviation. Both assertion and reason are true, and R correctly explains A.
Assertion (A): When a light wave travels from a rarer to a denser medium, it loses energy.
Reason (R): When a light wave travels from a rarer to a denser medium, it loses speed and energy carried by the wave is proportional to its speed.
The energy of a light wave depends on its frequency \(E=h\nu\), which remains constant when light travels between different media. While the speed changes, the energy does not. Therefore, both assertion and reason are false.