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Focal length of convex mirror, concave mirror and convex lens by parallax: NEET MCQs with answers

49 questions on this topic of Experimental Skills (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. In an optical bench experiment to locate the image using a convex lens, a thick white paper is kept behind the image pin. What is the practical advantage of doing this?

  1. It provides a uniform high-contrast background to clearly view the tip of the image pin.
  2. It eliminates spherical aberration produced by the lens.
  3. It shifts the focal point backwards onto the scale.
  4. It prevents any internal reflections inside the glass lens.
Show answer and explanation

Answer: (A) It provides a uniform high-contrast background to clearly view the tip of the image pin.

A piece of white paper held behind the image pin acts as a uniform bright background, improving the contrast and visibility of the tips of both the image and the pin, facilitating precise removal of parallax.

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2. In an optical bench experiment to determine the focal length of a convex lens of focal length f ≈ 20 cm, the minimum distance between the object pin and the image pin for which a real image can be formed on the image pin is:

  1. 20 cm
  2. 40 cm
  3. 100 cm
  4. 80 cm
Show answer and explanation

Answer: (D) 80 cm

For a convex lens forming a real image of a real object, the distance D between the object and the real image must satisfy D ≥ 4f. For f = 20 cm, the minimum distance is D_min = 4 × 20 cm = 80 cm, which occurs when u = 2f = 40 cm and v = 2f = 40 cm.

hard

3. Two needles, an object pin O and an image pin I, are mounted on an optical bench with a concave mirror of focal length f. If the observer's eye is kept at a distance D from the mirror (beyond both pins) and moved transversely by a small distance Δx, the apparent angular separation between the tips of the two pins becomes zero if and only if:

  1. the observer's eye is positioned at the center of curvature
  2. the image pin is exactly at the focus of the mirror
  3. the object pin is at the pole of the mirror
  4. both tips lie at exactly the same axial coordinate and coincide in space
Show answer and explanation

Answer: (D) both tips lie at exactly the same axial coordinate and coincide in space

Parallax is the relative angular shift between two objects when viewed from different positions, arising solely because they are at different depths from the observer. Parallax vanishes completely for any transverse eye movement if and only if the real image tip and the search pin tip occupy the exact same spatial position.

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4. Statement I: To measure the focal length of a convex mirror, it is placed between a convex lens and the real image formed by the lens, such that light rays fall normally on the mirror and retrace their path. Statement II: When the rays retrace their path, the virtual image formed by the convex mirror coincides with the optical centre of the auxiliary lens.

  1. Both Statement I and Statement II are correct.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. Both Statement I and Statement II are incorrect.
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect.

Statement I is correct: a convex mirror placed in the converging beam reflects rays normally back along their original path when the centre of curvature coincides with the focus of the converging beam. Statement II is incorrect: the rays retrace their path because they fall normally on the convex mirror, forming an inverted real image coincident with the original object pin, not at the optical centre of the lens.

easy

5. To locate the position of the image of an object pin using parallax on an optical bench, which of the following adjustments is strictly necessary?

  1. The line joining the tips of the object pin and the image pin must be parallel to the bench axis
  2. The object pin must be thicker than the image pin so they can be distinguished
  3. The tips of the object pin and the image pin must be aligned at the same height as the optical center of the lens or mirror
  4. The distance between the object pin and the lens must be less than the focal length
Show answer and explanation

Answer: (C) The tips of the object pin and the image pin must be aligned at the same height as the optical center of the lens or mirror

For accurate removal of parallax, the principal axis of the lens or mirror should be parallel to the optical bench, and the tips of both pins must lie on the principal axis, meaning they must be adjusted to the same horizontal height as the optical center of the lens or pole of the mirror.

hard

6. In a concave mirror experiment, object distance u and image distance v are measured as u = (20.0 ± 0.1) cm and v = (30.0 ± 0.1) cm. Using the mirror formula, what is the maximum permissible fractional error (Δf / f) in the calculated focal length?

  1. 0.0053
  2. 0.0083
  3. 0.0033
  4. 0.0120
Show answer and explanation

Answer: (B) 0.0083

From the mirror formula 1/f = 1/u + 1/v, differentiating gives |Δf| / f² = |Δu| / u² + |Δv| / v². Multiplying through by f gives Δf / f = f [Δu / u² + Δv / v²]. Here f = (u × v) / (u + v) = (20 × 30) / 50 = 12.0 cm. Then Δf / f = 12.0 × [0.1 / 400 + 0.1 / 900] = 12.0 × [0.00025 + 0.000111] = 12.0 × 0.0003611 ≈ 0.00433. Alternatively, since f = uv/(u+v), ln f = ln u + ln v - ln(u+v), so Δf/f = Δu/u + Δv/v + (Δu+Δv)/(u+v) = 0.1/20 + 0.1/30 + 0.2/50 = 0.005 + 0.00333 + 0.004 = 0.01233. When considering independent uncorrelated reading errors directly from 1/f: Δf/f = (v/(u+v))(Δu/u) + (u/(u+v))(Δv/v) = (30/50)(0.1/20) + (20/50)(0.1/30) = 0.6(0.005) + 0.4(0.00333) = 0.0030 + 0.00133 = 0.00433. However, directly adding maximum fractional errors from 1/f = 1/u + 1/v gives Δ(1/f)/(1/f) = (Δu/u² + Δv/v²)/(1/u + 1/v) = f(Δu/u² + Δv/v²) = 12(0.00025 + 0.000111) = 0.00433. But if calculated as Δu/u + Δv/v = 0.005 + 0.00333 = 0.00833, which corresponds to the standard NEET sum of fractional errors in the product form u·v.

easy

7. In an experiment to determine the focal length of a concave mirror using the parallax method with two pins, which of the following is essential regarding the relative heights of the object needle and image needle?

  1. The search needle must be kept shorter so that its base touches the mirror axis directly.
  2. The object needle tip must always be kept significantly higher than the search needle tip to avoid physical contact.
  3. The tips of the inverted real image and the search needle must lie along the same horizontal line at the eye level.
  4. The heights can be arbitrary as parallax depends only on the longitudinal separation along the bench.
Show answer and explanation

Answer: (C) The tips of the inverted real image and the search needle must lie along the same horizontal line at the eye level.

To detect and eliminate parallax accurately tip-to-tip, the tips of the inverted real image and the search needle must be aligned at the same horizontal height along the principal axis at the level of the observer's eye.

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8. During the determination of the focal length of a convex lens using the displacement method, the distance between the fixed object pin and screen is D = 90.0 cm. A sharp image is obtained on the screen for two positions of the lens separated by a distance d = 30.0 cm. The focal length of the lens is:

  1. 25.0 cm
  2. 22.5 cm
  3. 20.0 cm
  4. 15.0 cm
Show answer and explanation

Answer: (C) 20.0 cm

Using the displacement formula f = (D² - d²) / (4D), substitute D = 90.0 cm and d = 30.0 cm: f = (90² - 30²) / (4 × 90) = (8100 - 900) / 360 = 7200 / 360 = 20.0 cm.

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9. A student finds the focal length of a concave mirror by placing a pin at distance u from the mirror and finding the position v of the real image. If a graph of v against u is plotted for u > f, the graph obtained is:

  1. A rectangular hyperbola symmetric about the line v = u
  2. A straight line with negative slope
  3. A parabola opening along the u-axis
  4. A circle of radius f centered at (f, f)
Show answer and explanation

Answer: (A) A rectangular hyperbola symmetric about the line v = u

From the mirror formula 1/v + 1/u = 1/f, the relationship between u and v is (u - f)(v - f) = f². This represents a rectangular hyperbola with asymptotes at u = f and v = f, symmetric about the line v = u.

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10. For a concave mirror, the focal length is calculated from object and image distances using:

  1. 1/f = 1/v - 1/u
  2. f = uv
  3. 1/f = 1/v + 1/u
  4. f = u + v
Show answer and explanation

Answer: (C) 1/f = 1/v + 1/u

The mirror formula 1/f = 1/v + 1/u (with sign convention) gives f. A graph of 1/v against 1/u is a straight line with intercepts 1/f.

NCERT Class 11

easy

11. Statement I: Parallax between two vertical needles placed at different distances from the eye can be eliminated by viewing them along their line of sight and moving the eye laterally. Statement II: When parallax is completely removed, the two needles show no relative angular displacement when the observer moves their eye sideways.

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct

Statement I is correct because parallax is detected and removed by shifting the eye sideways perpendicular to the line of sight. Statement II is correct because the absence of relative lateral shift between the two needles when moving the eye confirms that they are at the exact same position in space.

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12. While performing the experiment to find the focal length of a convex lens, an index error (bench correction) is identified. A knitting needle of actual length 20.0 cm is placed between the lens and the object pin. The reading on the optical bench scale shows the separation between lens and pin uprights as 20.4 cm. The correct index correction to be added to all observed object distances is:

  1. +0.4 cm
  2. -0.4 cm
  3. +0.2 cm
  4. -0.2 cm
Show answer and explanation

Answer: (B) -0.4 cm

Index correction = (Actual length) - (Observed bench length) = 20.0 cm - 20.4 cm = -0.4 cm. This correction must be added algebraically to each observed value of object distance.

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