Physics Chapter: Focal Length and Snell's Law

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Questions and Answers

How much time does it take for the sun to shift by 1 degree when viewed from Earth?

40 minutes

4 minutes (correct)

1 minute

10 minutes

What path should the lifeguard take to minimize the time to reach the drowning child?

A path that satisfies Snell's law (correct)

Any random path GXC

Path GBC in water

Direct path GAC

What determines the minimum time for the lifeguard to reach the child?

The depth of the pool

The length of the pool

The angle of incidence and Snell's law (correct)

The swimming speed of the lifeguard

What occurs when light travels from an optically denser medium to a rarer medium at the interface?

Partial reflection and refraction Signup and view all the answers

In Snell's law, what does the ratio $\frac{v_1}{v_2}$ represent?

The refractive index of the medium Signup and view all the answers

What is the relationship between the running speed of the lifeguard on ground and their swimming speed?

Running speed is higher than swimming speed Signup and view all the answers

What must be minimized for the lifeguard to reach the child in the shortest time?

The total travel time from G to C Signup and view all the answers

How does the refractive index relate to the behavior of light at the boundary of two mediums?

It influences both reflection and refraction Signup and view all the answers

What is the principal focus of a concave mirror?

The point where reflected rays converge Signup and view all the answers

What does the focal length of a mirror denote?

The distance between the focus and the center of curvature Signup and view all the answers

For a convex mirror, what happens to the reflected rays?

They appear to diverge from a point Signup and view all the answers

How is the focal length of a spherical mirror mathematically expressed in terms of the radius of curvature?

f = R/2 Signup and view all the answers

In the case of paraxial rays, what approximation can be made for small angles?

tan θ ≈ θ Signup and view all the answers

What role does the center of curvature 'C' play in relation to a ray striking the mirror?

It is used to measure the angle of incidence Signup and view all the answers

What geometric shape do the rays follow when they reflect off a concave mirror?

They follow a converging path towards a point Signup and view all the answers

What is the relationship between the angles of incidence and reflection for a ray reflecting off a spherical mirror?

They are equal Signup and view all the answers

What is the primary requirement for fabricating optical fibres?

Very little absorption of light Signup and view all the answers

In the context of lenses, what is a thin lens defined as?

An optical medium bounded by two surfaces, at least one of which is spherical Signup and view all the answers

What happens to light when it travels through quality silica glass fibres?

Approximately 95% of the light is transmitted over 1 km Signup and view all the answers

How can a small part of a spherical surface be treated for refraction analysis?

As a flat surface Signup and view all the answers

What does the lens maker’s formula relate to?

Image formation by a single spherical surface in a lens Signup and view all the answers

What is the role of the normal line at a point of incidence on a spherical surface?

It passes through the center of curvature Signup and view all the answers

What approximation is made for small apertures in spherical surfaces?

Small angle approximation Signup and view all the answers

When comparing the efficiency of light transmission in optical fibres versus ordinary window glass, optical fibres perform:

Better with significantly lower absorption Signup and view all the answers

What unit is used to measure illuminance?

lux Signup and view all the answers

In the equation $E = \frac{I}{r^2}$, what does 'r' represent?

The distance from the source Signup and view all the answers

What does the term luminance refer to?

The brightness of emitting or reflecting flat surfaces Signup and view all the answers

What is the radius of curvature of the spherical glass surface in the provided example?

20 cm Signup and view all the answers

According to Snell's Law, how is the relationship between refractive indices and angles expressed?

n1 sin i = n2 sin r Signup and view all the answers

What values are substituted for 'OM', 'MI', and 'MC' in Equation (9.15) using the Cartesian sign convention?

OM = -u, MI = +v, MC = +R Signup and view all the answers

What is the relationship described by Equation (9.16) regarding object and image distances?

It connects object and image distance with refractive index and radius of curvature Signup and view all the answers

If the distance of the light source from the spherical glass surface is 100 cm, what is the value of 'u' used in the example?

-100 cm Signup and view all the answers

What is the significance of the point where the image of an object placed at infinity is formed?

It is known as the focus of the lens. Signup and view all the answers

What does DI1 represent in the context of lens image formation?

The virtual object distance for the second surface. Signup and view all the answers

According to the equations presented, what is true for a thin lens regarding BI1 and DI1?

BI1 and DI1 are equal. Signup and view all the answers

If OB approaches infinity, what does the equation for the focal length simplify to?

f approaches n1/(n2-n1) Signup and view all the answers

What is the variable DI representing in the equations related to lens optics?

The image distance from the lens. Signup and view all the answers

In the equations governing lens image formation, how is the distance DI1 measured?

Against the direction of incident light. Signup and view all the answers

What does the variable f signify in the context of lens optics?

The focal length of the lens. Signup and view all the answers

What do the equations (9.17) and (9.18) illustrate in lens optics?

The behavior of light as it passes through multiple interfaces. Signup and view all the answers

Study Notes

Focal Length

A concave mirror converges a parallel beam of light to a single point called the principal focus
A convex mirror causes a parallel beam of light to diverge and appear to come from a single point called the principal focus
The focal length of a mirror is the distance between the principal focus and the pole of the mirror
The focal length (f) of a mirror is half its radius of curvature (R): f = R/2
The focal plane is a plane passing through the principal focus perpendicular to the principal axis where reflected rays from a parallel beam of light, at any angle to the principal axis, converge.

Snell's Law and the Drowning Child

The shortest path for a lifeguard to get to a drowning child in a swimming pool is not a straight line.
The lifeguard should enter the water where Snell's Law is satisfied.
Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media, which is also the refractive index.
For any wave, particle, or object moving between two mediums and two velocities follows Snell's Law to minimize the time it takes to travel between them.

Total Internal Reflection

When light travels from an optically denser medium to a rarer medium, it is partly reflected back into the denser medium and partly refracted into the rarer medium
This reflection is called internal reflection.
Optical fibers utilize total internal reflection to transport light across long distances with minimal loss by transmitting light along the core of the fiber, surrounded by a cladding with a lower refractive index.

Refraction at a Spherical Surface

The refractive index is the ration of the speed of light in vacuum to its speed in the medium.
The geometry of image formation by a spherical surface is described by the following equation: n1 / OM + n2 / MI = (n2 - n1) / MC
The equation is derived using Snell's Law and the small angle approximation.
Using the Cartesian sign convention, we can put the value of object distance (u) as negative, image distance (v) as positive when it is real, and the radius of curvature (R) as positive when the surface is concave, and negative when it is convex.

Refraction by a Lens

A thin lens is a transparent optical medium bounded by two surfaces, at least one of which is spherical.
The lens maker’s formula is derived by applying the equation for image formation by a single spherical surface to the two surfaces of the lens (n1 / OB + n1 / DI = (n 2 - n1) / BC1 + (n 2 - n1) / DC2).
The lens formula is a special case of the lens maker’s formula when the object is placed at infinity (n1 / f = (n 2 - n1) / BC1 + (n 2 - n1) / DC2)
The focal length of a lens is the distance between the focal point and the lens.

Illuminance and Luminance

Illuminance measures the luminous flux incident per unit area.
Luminance characterizes the brightness of emitting or reflecting flat surfaces

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Description

Explore concepts of focal length in mirrors and the application of Snell's Law through a practical scenario with a lifeguard. This quiz covers the fundamentals of light convergence, focal lengths, and the refraction principles essential for understanding optics. Test your knowledge and understanding of these key physics topics.