A parabolic reflector is 5 cm deep and its diameter is 20 cm. How far is its focus from the vertex?
Given: Parabolic reflector is 5 cm deep & its diameter is 20 cm
Need to find: Distance of its focus from the vertex.
Reflector is $5 \mathrm{~cm}$ deep, i.e., $O D=5 \mathrm{~cm}$
Diameter of the mirror is $20 \mathrm{com}$, i.e., $B C=20 \mathrm{~cm}$
Let, the equation of the parabola is $y^{2}=4 a x$, where a is the distance of the focus from the vertex.
The $x$-coordinate of the points $B$ and $C$ is 5 .
$\mathrm{D}$ is the middle point of $\mathrm{BC}$ which is upon the $\mathrm{x}$-axis.
So, we can say that $B D=C D=10 \mathrm{~cm}$.
So, the coordinate of the point $B$ is $(5,10)$
Putting the values of the equation,
$y^{2}=4 a x$
$\Rightarrow 100=4 a \times 5$
$\Rightarrow 20 a=100$
$\Rightarrow a=5$
That means, the focus is 5 cm far from the vertex.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,