What is Image Formation by Convex Mirror?

S6-SA3-0331

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

Image formation by a convex mirror describes how light rays reflect off its curved surface to create an image. Unlike flat mirrors, convex mirrors always form images that are virtual, erect (upright), and diminished (smaller than the actual object). This happens because convex mirrors diverge (spread out) parallel light rays after reflection.

Simple Example

Quick Example

Imagine you are looking at your reflection in the shiny, curved back of a spoon. The image you see is smaller than your actual face and appears upright. This is a simple example of how a convex mirror (like the back of the spoon) forms an image – it always makes things look smaller and standing straight up.

Worked Example

Step-by-Step

Let's find the position and nature of the image formed by a convex mirror when an object is placed 15 cm in front of it. The mirror has a focal length of 10 cm.

Step 1: Write down the given values and sign conventions. Object distance (u) = -15 cm (object is always placed to the left). Focal length (f) = +10 cm (focal length of a convex mirror is positive). We need to find image distance (v).

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Step 2: Use the mirror formula: 1/f = 1/v + 1/u.

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Step 3: Substitute the values into the formula: 1/10 = 1/v + 1/(-15).

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Step 4: Rearrange the equation to solve for 1/v: 1/v = 1/10 - 1/(-15) = 1/10 + 1/15.

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Step 5: Find a common denominator and add the fractions: 1/v = (3 + 2) / 30 = 5/30 = 1/6.

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Step 6: Invert to find v: v = +6 cm.

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Step 7: Determine the nature of the image using magnification (m = -v/u) if needed, or by the sign of v. Since v is positive (+6 cm), the image is formed behind the mirror. This means the image is virtual and erect.

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Answer: The image is formed 6 cm behind the mirror. It is virtual, erect, and diminished.

Why It Matters

Understanding convex mirrors is crucial for engineers designing vehicle rearview mirrors, allowing drivers to see a wider area. It's also vital in optics for creating specific lens systems in cameras and telescopes. This knowledge can lead to careers in automotive design, optical engineering, and even space technology.

Common Mistakes

MISTAKE: Students often use a negative sign for the focal length (f) of a convex mirror. | CORRECTION: The focal length (f) of a convex mirror is always taken as positive, as its focus is behind the mirror.

MISTAKE: Assuming the image formed by a convex mirror can be real and inverted. | CORRECTION: Convex mirrors ONLY form virtual, erect, and diminished images, regardless of the object's position.

MISTAKE: Confusing the mirror formula (1/f = 1/v + 1/u) with the lens formula. | CORRECTION: Remember the '+' sign in the mirror formula for image and object distances, unlike the '-' sign in the lens formula.

Practice Questions

Try It Yourself

QUESTION: A convex mirror has a focal length of 20 cm. If an object is placed at 40 cm from the mirror, where will the image be formed? | ANSWER: 13.33 cm behind the mirror.

QUESTION: An object of height 5 cm is placed 30 cm in front of a convex mirror with a radius of curvature of 20 cm. Calculate the height of the image. | ANSWER: 1.25 cm

QUESTION: A driver uses a convex rearview mirror with a focal length of 12 cm. If a car behind is 6 meters (600 cm) away, what is the magnification of the image of the car? | ANSWER: 0.0196 (approx. 0.02)

MCQ

Quick Quiz

Which of the following describes the image formed by a convex mirror?

Real, inverted, and magnified

Virtual, erect, and diminished

Real, erect, and diminished

Virtual, inverted, and magnified

The Correct Answer Is:

A convex mirror always forms an image that is virtual (cannot be projected on a screen), erect (upright), and diminished (smaller than the object), regardless of the object's position.

Real World Connection

In the Real World

You see convex mirrors every day! The rearview mirror on the passenger side of your family car or an auto-rickshaw is a convex mirror. It helps the driver see a wider area behind the vehicle, even though the objects appear smaller and farther away. Also, security mirrors in shops, like a Kirana store, are convex, giving a wide view of the shop floor.

Key Vocabulary

Key Terms

VIRTUAL IMAGE: An image that cannot be formed on a screen, appearing to be behind the mirror. | ERECT IMAGE: An upright image, meaning it's not inverted. | DIMINISHED IMAGE: An image that is smaller than the actual object. | FOCAL LENGTH: The distance between the pole of the mirror and its principal focus. | RADIUS OF CURVATURE: The radius of the sphere from which the mirror is a part.

What's Next

What to Learn Next

Now that you understand convex mirrors, try learning about 'Image Formation by Concave Mirrors'. This will help you compare and contrast how different curved mirrors behave and prepare you for understanding lenses!