An object is placed in front of a convex spherical glass surface ($n=1.5$ and radius of curvature $R$) at a distance of $4R$ from it. As the object is moved slowly close to the surface, the image formed is: A). always real B). always virtual C). first real and then virtual D). first virtual and then real

The correct answer is first real and then virtual. **Answer: first real and then virtual** \n Using the formula for refraction at a spherical surface: $\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2-n_1}{R}$.\nHere, $n_1=1$, $n_2=1.5$. Initially, $u=-4R$.\n$$\frac{1.5}{v} - \frac{1}{-4R} = \frac{1.5-1}{R} \Rightarrow \frac{1.5}{v} + \frac{1}{4R} = \frac{0.5}{R}$$\n$$\frac{1.5}{v} = \frac{2}{4R} - \frac{1}{4R} = \frac{1}{4R} \Rightarrow v = +6R \text{ (Real image)}$$\nIf the object is moved very close, say $u=-R$:\n$$\frac{1.5}{v} - \frac{1}{-R} = \frac{0.5}{R} \Rightarrow \frac{1.5}{v} = \frac{0.5}{R} - \frac{1}{R} = \frac{-0.5}{R} \Rightarrow v = -3R \text{ (Virtual image)}$$\nThus, the image is first real and then virtual.

CBSE 2025, Set 3 – Physics

When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction $90^\circ$ is called the critical angle $(i_c)$ for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2.\n\nRefraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation.\n\nLaws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.

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