Understanding the Velocity of an Image Formed by a Plane Mirror

The velocity of image in plane mirror describes how fast and in what direction the image appears to move when the object, the mirror, or both are in motion. Understanding this is crucial for JEE Main as it connects kinematics with ray optics, a high-scoring topic in competitive exams.

Imagine walking straight towards a mirror on the wall. You will notice the image approaches you, and if you run away, your image also retreats at the same rate. But what if you walk sideways, or the mirror itself moves? For JEE, knowing how to calculate these velocities prepares you for typical exam questions involving reflection and relative motion concepts.

Key Cases for Velocity of Image in Plane Mirror

The apparent speed and direction of an image in a plane mirror depend on how the object and mirror move. Let’s dissect the main scenarios often tested in JEE:

• Object moves perpendicular to mirror's surface
• Object moves parallel to plane mirror
• Object moves at an angle to the mirror
• Mirror itself is moving (parallel or at an angle)

Let’s explore each situation with simple logic and formulae.

Stationary Mirror: Types of Object Motion

When the mirror is fixed, all image movement depends on the object's velocity. Remember, a plane mirror always forms a virtual, erect image located the same distance behind the mirror as the object is in front.

If an object moves perpendicular to the mirror (toward or away):

• The image appears to move at equal speed but opposite direction.
• Formula: v_img = -v_obj, where v_obj is perpendicular speed.

If you move parallel to the plane mirror's surface, your image copies your motion:

• Same magnitude and direction as object
• No change in distance from the mirror
• Formula: v_img = v_obj (parallel component only)

If the motion is at some angle θ to the mirror, break the object's velocity into two components:

• Parallel to mirror: stays the same in the image
• Perpendicular to mirror: direction reverses in the image

Now, combine both using a vector approach:
v_img = v_parallel + (–v_{perpendicular})

For example, if a ball moves diagonally to a mirror, draw the two components, reverse the one facing the mirror, and add up the vectors to get the image's true motion. This vector approach is easy to apply when you practice questions from Vedantu’s JEE modules.

See related concept in object and image velocities.

Plane Mirror Moving: Relative Motion Approach

Now, let’s make it interesting — what if the mirror moves? This brings in relative velocity, a favourite concept in JEE questions. To analyse, always view the object’s speed with respect to the moving mirror, then mirror that effect in the image.

Common situations:

• Mirror moves parallel to its plane: Add mirror and object velocities first (relative to each other), then reverse the perpendicular component for the image.
• Mirror moves perpendicular to plane: Components along the perpendicular might not affect the image, depending on combined relative motion.
• Mirror moves at an angle: Resolve the mirror's movement into parallel and perpendicular, repeat above logic.

For an object with velocity v_obj and a mirror with velocity v_m (both parallel), the image’s absolute velocity becomes:
v_img = –v_obj + 2v_m

This formula is direct and is extremely useful in MCQs, especially when asked about a person running toward a moving lift mirror or a car reversing with a rear-view mirror in motion. Always keep track of directions by drawing quick diagrams — Vedantu teachers emphasise this in their video solutions for a reason!

For additional clarity, see the difference between mirror and lens on the Vedantu JEE Main portal.

Velocity of Image for Inclined Plane Mirror

Occasionally, questions set the plane mirror at an angle to the horizontal. Here, break every velocity (object and mirror) into components parallel and perpendicular to the mirror's surface.

Suppose the object velocity is v_o and the mirror makes angle θ with the ground:

• Component along mirror: v_ocosθ
• Perpendicular to mirror: v_osinθ
• Image velocity: v_ocosθ – v_osinθ (vector addition)

You can visualise this with a fast-moving puck gliding toward a slanted mirror — its image doesn’t follow the same straight path as the real object.

Key Formulas and Fast Revision Table

Here’s a concise table of all the formulae, ideal for last-minute JEE Main Physics revisions:

For deeper insight on magnification and crazy image tricks in plane and spherical mirrors, read detailed notes here.

Why Velocity of Image in Plane Mirror Is a JEE Must-Know

Questions on this topic test a mix of vectors, relative motion, and ray optics — high-yield areas in JEE Main Physics. Mastering velocity analysis for mirrors ensures you won’t fumble the kind of MCQ or assertion-reason problems appearing every year.

Vedantu’s JEE materials and online classes reinforce this topic with visual diagrams and past exam questions to help students secure crucial marks efficiently. Knowing when and how to decompose velocities, and apply the sign conventions quickly, is a vital exam hack for every aspirant.