A fluorescent lamp of length 1 m is placed horizontal at a depth of 1.2 m below a ceiling. A p

step 1 Hello and welcome to this video solution of Numerate. Here we are given a fluorescent lamp of le

A fluorescent lamp of length 1 m is placed horizontal at a...

A fluorescent lamp of length $1 \mathrm{~m}$ is placed horizontal at a depth of $1.2 \mathrm{~m}$ below a ceiling. A plane mirror of length $0.6 \mathrm{~m}$ is placed below the lamp parallel to and symmetric to the lamp at a distance $2.4 \mathrm{~m}$ from it. The length of the reflected patch of light on the ceiling is: (a) $3 \mathrm{~m}$ (b) $4 \mathrm{~m}$ (c) $7 \mathrm{~m}$ (d) none of these

A fluorescent lamp of length $1 \mathrm{~m}$ is placed horizontal at a depth of $1.2 \mathrm{~m}$ below a ceiling. A plane mirror of length $0.6 \mathrm{~m}$ is placed below the lamp parallel to and symmetric to the lamp at a distance $2.4 \mathrm{~m}$ from it. The length of the reflected patch of light on the ceiling is:
(a) $3 \mathrm{~m}$
(b) $4 \mathrm{~m}$
(c) $7 \mathrm{~m}$
(d) none of these

Key Concepts

Plane Mirror Reflection

This concept involves understanding how light reflects off a flat, reflective surface. A plane mirror produces images that appear as if they are located behind the mirror at the same distance as the object is in front. It is fundamental to predicting where the reflection of an object will appear and how its size and orientation are affected by the mirror.

Law of Reflection

The law of reflection states that the angle of incidence is equal to the angle of reflection, with both angles measured from the normal to the surface at the point of incidence. This principle is the bedrock of understanding how light rays bounce off mirrors and is essential for tracing the path of light in any system involving reflections.

Ray Diagram Analysis

Ray diagrams are graphical representations used to trace the paths that light rays take in optical systems. They help in visualizing how light from an object, such as a fluorescent lamp, interacts with reflective surfaces and forms images on surfaces like ceilings. This analysis often employs the law of reflection to determine the exact locations and extents of the light patches.

Geometric Relationships in Optics

Geometric principles, such as the use of similar triangles, are crucial in optical problems to relate distances, lengths, and angles. When light reflects off a plane mirror, similar triangles can be used to connect the positions of the lamp, mirror, and ceiling, enabling the calculation of the dimensions of the reflected image. These relationships simplify complex optical setups into manageable geometric problems.

Transcript

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