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): When an object is placed between two plane parallel mirrors, all the images formed are of equal intensity.
Reason (R): In above situation of two plane parallel mirrors, only two images are possible.
Assertion (A) is false. Image intensity decreases with each reflection due to absorption.
Reason (R) is false. An infinite number of images are formed between two parallel plane mirrors.
Therefore, both (A) and (R) are false.
Assertion (A): The focal length of spherical mirror does not depend on the wavelength of light.
Reason (R): The number of wavelengths in the visible region of spectrum are infinite.
Assertion (A) is true as focal length of spherical mirrors depends only on its radius of curvature, not refractive index or wavelength.
Reason (R) is false. The visible spectrum is a continuous range, not an infinite countable number of wavelengths.
So, (A) is true but (R) is false.
Assertion (A): A real object is placed on the optic axis of a lens such that an erect image of twice the size of the object is obtained. The lens must then be a convergent lens.
Reason (R): Erect image of a real object can be produced by a concave lens and also by a convex lens.
Assertion (A) is true. A real object producing an erect, magnified image (like (2) times) can only happen with a convergent (convex) lens when the object is between (F) and (O).
Reason (R) is true. Concave lenses produce erect, diminished images; convex lenses produce erect, magnified images under specific conditions.
Both (A) and (R) are true, but (R) does not explain the magnification condition in (A).
Assertion (A): A real object is placed on the optic axis of a lens such that magnification of the image is (+0.5). The lens must then be a divergent lens.
Reason (R): A concave lens always produces a virtual image of a real object.
Assertion (A) is true. (m = +0.5) indicates an erect and diminished image. For a real object, only a divergent (concave) lens produces such an image.
Reason (R) is true. A concave lens always forms a virtual, erect, and diminished image for a real object.
(R) correctly explains (A) because a concave lens's image characteristics match the given magnification.
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): 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.