63 questions on this topic of Optics (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.
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Answer: (B) (n - 1)f
For a convex mirror, magnification m = +1/n and focal length is +f. Using the formula m = f / (f - u), we have 1/n = f / (f - u). Solving gives f - u = nf, which leads to -u = (n - 1)f. Thus, the object distance from the mirror is (n - 1)f.
Answer: (A) 30 cm
1/v + 1/u = 1/f with u = −60 cm and f = −20 cm gives v = −30 cm: a real image 30 cm in front of the mirror.
Answer: (B) 0.31 m s⁻¹
Radius R = 4.0 m ⇒ f = +2.0 m. Distance u = -6.0 m. The image position v is given by 1/v = 1/f - 1/u = 1/2 - (-1/6) = 1/2 + 1/6 = 4/6 = 2/3 m⁻¹, so v = 1.5 m. The longitudinal speed of the image is v_img = (v/u)² × v_obj = (1.5 / 6.0)² × 5.0 = (1/4)² × 5.0 = 5.0 / 16 ≈ 0.31 m s⁻¹.
Answer: (A) Both Statement I and Statement II are correct.
The derivation of the standard mirror formula 1/v + 1/u = 1/f assumes paraxial rays, where the angles made with the principal axis are small so that tan θ ≈ sin θ ≈ θ. Marginal rays (rays far from the principal axis) focus closer to the pole than paraxial rays, causing spherical aberration. Therefore, both statements are correct.
Answer: (A) Both Statement I and Statement II are true
The focal length of a spherical mirror is purely a geometric property given by f = R/2 for paraxial rays and depends only on its radius of curvature. Because reflection depends purely on equal angles of incidence and reflection regardless of the medium's refractive index, both statements are true.
Answer: (A) 30 cm
Using the formula m = f / (f - u) for real images: initially, -3 = -f / (-f - (-u₁)), which means m = f / (u - f) = 3, so u₁ - f = f/3 or u₁ = 4f/3. In the second position, the object is moved 5 cm away, so u₂ = u₁ + 5. Here m = 2, so u₂ - f = f/2 or u₂ = 3f/2. Subtracting gives u₂ - u₁ = 3f/2 - 4f/3 = f/6 = 5 cm, giving f = 30 cm.
Answer: (A) -12 cm
Magnification m = -v/u = -4, which means v = 4u. Since both object and image are in front of the mirror (real image), the separation between them is |v - u| = 4u - u = 3u. We are given 3u = 45 cm, so u = 15 cm, and thus v = 60 cm. Using the mirror formula with signs: 1/f = 1/(-60) + 1/(-15) = -5/60 = -1/12 cm⁻¹, which gives f = -12 cm.
Answer: (D) 4R / 3
With the top surface acting as a concave mirror of radius R (focal length f = R/2), the source is at distance u = 2R from the pole. From 1/v + 1/u = 1/f, we have 1/v - 1/(2R) = -2/R, which yields v = -2R/3 from the top pole. Since the source is at distance 2R from the pole, the separation between the source and its image is 2R - 2R/3 = 4R/3.
Answer: (C) (u - f)⁻³
The image position is v = f u / (u - f). The velocity of the image is v_i = dv/dt = - [f² / (u - f)²] du/dt = [f² / (u - f)²] v₀. Differentiating with respect to time to get acceleration gives a_i = dv_i/dt = -2 f² (u - f)⁻³ (du/dt) v₀ = 2 f² v₀² (u - f)⁻³. Therefore, the acceleration is proportional to (u - f)⁻³.
Answer: (A) L × [f / (u - f)]²
Differentiating the mirror formula 1/v + 1/u = 1/f with respect to u gives -dv/v² - du/u² = 0, so dv = - (v/u)² du. Here, du = L, and since v/u = f / (u - f), the longitudinal magnification is (v/u)² = [f / (u - f)]². Therefore, the length of the image is L × [f / (u - f)]².
Answer: (C) 33.3 cm
1/v + 1/u = 1/f with u = −100 cm and f = −25 cm gives v = −33.3 cm: a real image 33.3 cm in front of the mirror.
Answer: (C) f
The focal length of a spherical mirror depends only on its radius of curvature (f = R/2) and the law of reflection, which is independent of the surrounding medium. Hence, its focal length remains unchanged at f.