Concave & Convex Lenses: Definitions, Formula, Magnification, Practice Problems & FAQs

Concave & Convex Lenses: Complete Guide

Understanding definitions, formula, magnification, practice problems, and FAQs.

Table of Contents

• 1. Introduction
• 2. Convex Lenses
• 3. Concave Lenses
• 4. Related Terms
• 5. Lens Formula
• 6. Magnification
• 7. Practice Problems
• 8. FAQs

1. Introduction

A lens is a transparent optical element with two curved surfaces that refract light to converge or diverge rays. There are two main types:

• Convex lens: Converging, thick at center
• Concave lens: Diverging, thin at center

2. Convex Lenses

A convex lens has two outward-curved surfaces. Parallel rays converge to the principal focus. It can form both real and virtual images depending on object placement.

A convex lens is thin at edges and thicker at center.

3. Concave Lenses

A concave lens has inward-curved surfaces. Parallel rays diverge as if they originate from the principal focus on the same side as the object. It only forms virtual, upright, diminished images.

A concave lens is thick at edges and thinner at center.

4. Related Terms

• Center of curvature: Center of the sphere for each surface (two per lens).
• Radius of curvature: Radius of that sphere.
• Optical center: Point through which rays pass undeviated.
• Principal axis: Line through the two centers of curvature.
• Principal focus: Point where parallel rays converge (convex) or appear to diverge (concave).

5. Lens Formula

The relation between object distance (u), image distance (v), and focal length (f) is:

1/f = 1/v – 1/u

Sign convention: Object and image distances measured from lens; same direction as incident light positive; opposite negative.

6. Magnification

Magnification (m) is the ratio of image height (h_i) to object height (h_o):

m = h_i / h_o = v / u

Positive m indicates upright image; negative inverted.

7. Practice Problems

Q1.

An object 5 cm tall is placed 20 cm from a convex lens of focal length 10 cm. Find the image distance and height.

Solution:

Using 1/f = 1/v – 1/u → 1/10 = 1/v – 1/(-20) → 1/v = 1/10 + 1/20 = 3/20 → v = 20/3 ≈ 6.67 cm

Magnification m = v/u = (20/3) / (–20) = –1/3 → h_i = m·h_o = –1/3 × 5 cm = –1.67 cm

The image is 6.67 cm on opposite side, inverted, height 1.67 cm.

Q2.

A concave lens of focal length –15 cm forms an image 10 cm from the lens. Find object distance.

Solution:

1/f = 1/v – 1/u → 1/(–15) = 1/(–10) – 1/u → –1/15 = –1/10 – 1/u → 1/u = –1/10 + 1/15 = (–3 + 2)/30 = –1/30 → u = –30 cm

Object is 30 cm in front of lens.

Q3.

An image is upright and half the size of a 12 cm object. Identify the lens and its magnification.

Solution:

m = h_i/h_o = ½ = 0.5 (positive). Positive upright, so lens is concave. Magnification = +0.5.

8. FAQs

Q1. What is the focal length of a plane glass plate?

A plane plate neither converges nor diverges light, so its focal length is infinite.

Q2. Which lens corrects hypermetropia?

Hypermetropia (farsightedness) is corrected with a convex lens to converge rays onto the retina.

Q3. How to identify convex vs. concave by appearance?

Convex is thinner at edges, thicker at center. Concave is thicker at edges, thinner at center.

Q4. What when a convex and concave lens of equal focal length are combined?

Their powers cancel, resulting in zero net power, behaving like a plane glass plate.