If a real and inverted image is formed by a convex lens on a screen 20cm away from the lens, and the object is placed 30cm from the lens, what is the focal length of the lens according to the lens formula?

Appeared in: RRB Nsg. Superintendent-2026 (Shift -3rd)

Explanation

The lens formula, 1/f = 1/v - 1/u, is used to find the focal length (f) from the object distance (u) and image distance (v).
According to the Cartesian sign convention, the object distance (u) is taken as negative (-30 cm) because it is placed on the left side of the lens.
The image distance (v) is taken as positive (+20 cm) because a real image is formed on the right side of the lens.
Substituting the values: 1/f = 1/(+20) - 1/(-30) = 1/20 + 1/30.
Solving the equation gives 1/f = (3+2)/60 = 5/60 = 1/12.
Therefore, the focal length (f) is +12 cm. The positive sign is characteristic of a convex (converging) lens.

Option B: This value represents the image distance (v), not the focal length. It incorrectly assumes the focal length is the same as the image distance without applying the lens formula.
Option C: This value is the result of a calculation error. For instance, incorrectly subtracting the fractions (1/20 - 1/30 = 1/60) or misplacing the signs would lead to an incorrect answer.
Option D: This value is also a result of a calculation error or a misunderstanding of the sign convention. For example, if both u and v were taken as positive, the result would be incorrect.

Visual 1: Ray Diagram - A diagram illustrating the formation of a real, inverted image by a convex lens. It shows the principal axis, optical center, focal points (f), and how rays from an object placed beyond 'f' converge to form an image on the opposite side.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Lens Formula and Sign Convention in Optics as background academic context rather than a clinical decision trigger.
Understanding lens optics is fundamental to comprehending how the human eye works, as the eye's lens is a converging lens system that focuses light onto the retina.
The principles of focal length and image formation are essential for understanding and correcting refractive errors like myopia (nearsightedness) and hyperopia (farsightedness) using corrective lenses (glasses or contacts).
Nurses performing vision screenings use charts (like the Snellen chart) placed at a standard distance (e.g., 20 feet), which relates to the optical principles of forming a clear image on the retina.

How to Approach the Question

First, identify the given parameters from the question: image distance (v = 20 cm) and object distance (u = 30 cm). Note that the image is 'real and inverted'.
Second, apply the standard sign convention for lenses. The object distance (u) is always negative. For a real image formed by a convex lens, the image distance (v) is positive. So, u = -30 cm and v = +20 cm.
Third, recall the lens formula: 1/f = 1/v - 1/u.
Fourth, substitute the values with their correct signs into the formula: 1/f = 1/(+20) - 1/(-30).
Fifth, simplify the expression: 1/f = 1/20 + 1/30.
Finally, solve the equation for the focal length (f) by finding a common denominator and inverting the result. This will lead to the correct answer.

Concept Tested & Keywords

Concept Tested: Lens Formula and Sign Convention in Optics
Stem keywords: real and inverted image, convex lens, screen, 20 cm away, object, 30 cm from the lens, focal length, lens formula
Lead-in keywords: what is

QnOrLF4Ye4VuDPQoup44yF

Practise the full RRB Nsg. Superintendent-2026 (Shift -3rd)

Attempt every question from this paper in a timed mock, then review the full solution for each one.