Reflection and Spherical Mirrors

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Questions and Answers

According to the laws of reflection, what is the relationship between the angle of incidence and the angle of reflection?

The angle of reflection is inversely proportional to the angle of incidence.
The angle of reflection is always less than the angle of incidence.
The angle of reflection is always greater than the angle of incidence.
The angle of reflection is equal to the angle of incidence. (correct)

If an incident ray, reflected ray, and the normal to the reflecting surface do not all lie in the same plane, what can be said about the reflection?

The reflection is specular.
The reflection is diffused.
The laws of reflection are not obeyed. (correct)
The laws of reflection are still obeyed.

For a spherical mirror, what line is considered the normal at any point on the surface?

The principal axis of the mirror.
The line joining the pole of the mirror to the point.
The line joining the center of curvature to the point. (correct)
The tangent to the surface at that point.

What is the principal axis of a spherical mirror defined as?

The line connecting the pole and the center of curvature. (D) Signup and view all the answers

When deriving formulas for reflection using spherical mirrors, what is the primary purpose of adopting a sign convention?

To ensure consistency and accuracy in measurements and calculations. (C) Signup and view all the answers

In the Cartesian sign convention, which of the following is a standard practice?

Measuring all distances from the pole of the mirror. (C) Signup and view all the answers

How does the normal at the point of incidence relate to the tangent at that point on a curved reflecting surface?

The normal is perpendicular to the tangent. (C) Signup and view all the answers

If a light ray strikes a curved mirror such that the angle of incidence is $30$ degrees, what is the angle between the reflected ray and the tangent to the mirror's surface at the point of incidence?

$60$ degrees (D) Signup and view all the answers

An object is placed 10 cm in front of a mirror with a focal length of -7.5 cm. What is the nature of the image formed?

Real, inverted, and magnified. (A) Signup and view all the answers

If an object is placed 5 cm in front of a mirror with a focal length of -7.5 cm, what are the characteristics of the image formed?

Virtual, erect, and magnified. (A) Signup and view all the answers

A jogger is running towards a parked car at a constant speed. The side view mirror of the car has a radius of curvature of 2 m. When the jogger is 39 m away, what is the approximate speed of the jogger's image?

1/280 m/s (C) Signup and view all the answers

A car's side view mirror has a radius of curvature $R = 2$ meters. Using the mirror equation, $v = \frac{fu}{u-f}$, where $u = -39$ meters. If the jogger moves at 5 m/s, find the new image position $v'$ after 1 second.

$\frac{34}{35}$ m (B) Signup and view all the answers

A car's side view mirror has a radius of curvature $R = 2$ meters and the jogger is running at 5 m/s. If the jogger is initially 39 meters away, calculate the average speed of the image when the jogger is between 39 meters and 34 meters from the mirror.

$\frac{1}{280}$ m/s (A) Signup and view all the answers

What is the relationship between the angle of incidence ($\theta$) and the angle between the principal axis and the line connecting the center of curvature to the point of incidence ($2\theta$) in the context of paraxial rays reflecting off a spherical mirror?

The angle between the principal axis and the line connecting the center of curvature to the point of incidence is approximately twice $\theta$. (C) Signup and view all the answers

Given a spherical mirror with a radius of curvature (R), what is the focal length (f) of the mirror, assuming paraxial rays?

$f = R/2$ (C) Signup and view all the answers

Under what conditions is the approximation $\tan(\theta) \approx \theta$ valid when analyzing the behavior of light rays interacting with spherical mirrors?

When the angle $\theta$ is small, which is true for paraxial rays. (B) Signup and view all the answers

In the derivation of the relationship between focal length (f) and radius of curvature (R) for a spherical mirror, why is point D considered to be very close to point P?

Because we are considering paraxial rays, which are close to the principal axis. (A) Signup and view all the answers

What is the primary distinction between a real and a virtual image formed by a spherical mirror?

Real images are formed by actual convergence of light rays, while virtual images appear to diverge from a point. (D) Signup and view all the answers

What does it signify when rays emanating from a point on an object do not actually meet after reflection from a spherical mirror, but appear to diverge from a point when produced backwards?

The image formed is virtual and located behind the mirror. (A) Signup and view all the answers

Why is it sufficient to trace only two rays emanating from a point on an object to determine the image location after reflection from a spherical mirror?

Because all rays from a single point converge to the same image point in ideal conditions. (B) Signup and view all the answers

Consider an object placed in front of a concave spherical mirror. If two rays are traced from a point on the object, one parallel to the principal axis and another passing through the center of curvature, how can their intersection point after reflection be used?

It locates the position of the image point corresponding to the initial point on the object. (A) Signup and view all the answers

When light travels from a denser to a rarer medium, at what angle of incidence does the angle of refraction become /2?

Critical angle (D) Signup and view all the answers

A light ray is incident from water (refractive index = 1.33) to air (refractive index = 1). What is the critical angle beyond which total internal reflection occurs?

$48.8^\circ$ (A) Signup and view all the answers

Why does a tank of water appear shallower than its actual depth when viewed from above?

Refraction of light causing an apparent shift in the position of the tank bottom (D) Signup and view all the answers

A ray of light passes through a glass slab with parallel sides. What is the relationship between the incident ray and the emergent ray?

The emergent ray is parallel to the incident ray but has undergone a lateral shift. (D) Signup and view all the answers

Under what conditions does total internal reflection occur?

Light travels from a denser to a rarer medium and the angle of incidence is greater than the critical angle. (A) Signup and view all the answers

What happens to the intensity of a light ray when it undergoes total internal reflection?

The intensity of the reflected ray is equal to the intensity of the incident ray. (C) Signup and view all the answers

In which of the cases will the light ray not experience any refraction?

Light traveling from air to water, striking the surface perpendicularly. (B) Signup and view all the answers

How does the apparent depth of an object submerged in water change as the viewing angle moves from normal (directly overhead) to oblique (at an angle)?

The apparent depth increases. (B) Signup and view all the answers

When light travels from medium 1 to medium 2, the refractive index of medium 2 with respect to medium 1 ($n_{21}$) is greater than 1. What can be concluded about the angle of refraction ($r$) and the optical density of medium 2?

$r < i$ and medium 2 is optically denser than medium 1 (A) Signup and view all the answers

The refractive index of medium A with respect to medium B is $n_{AB}$, and the refractive index of medium B with respect to medium A is $n_{BA}$. Which of the following relationships is correct?

$n_{AB} = 1/n_{BA}$ (B) Signup and view all the answers

A ray of light is incident from air onto a rectangular slab of glass. Which of the following statements concerning the ray's behavior as it exits the slab is correct, assuming the sides of the slab are parallel?

The outgoing ray is parallel and laterally displaced relative to the incoming ray. (B) Signup and view all the answers

The refractive index of medium 3 with respect to medium 1 is represented by $n_{31}$. If the refractive index of medium 3 with respect to medium 2 is $n_{32}$ and the refractive index of medium 2 with respect to medium 1 is $n_{21}$, how is $n_{31}$ related to $n_{32}$ and $n_{21}$?

$n_{31} = n_{32} * n_{21}$ (B) Signup and view all the answers

What is a key difference between optical density and mass density?

Optical density is the ratio of the speed of light in two media, while mass density is mass per unit volume. (D) Signup and view all the answers

Suppose a light ray is traveling from water (refractive index $n_w = 1.33$) into diamond (refractive index $n_d = 2.42$). According to Snell's law, what happens to the angle of refraction compared to the angle of incidence?

The angle of refraction is less than the angle of incidence; the ray bends towards the normal. (A) Signup and view all the answers

A light ray is incident on a glass slab at an angle of incidence i. The refractive index of the glass is n. If the angle of refraction inside the glass is r, which of the following expressions correctly relates i, r, and n?

$sin(i) = n * sin(r)$ (A) Signup and view all the answers

In a compound microscope, what is the primary function of the objective lens?

To form a real, inverted, and magnified image, which then serves as the object for the eyepiece. (A) Signup and view all the answers

Consider three media: A, B, and C. The refractive index of A with respect to B is 1.5, and the refractive index of B with respect to C is 0.8. What is the refractive index of A with respect to C?

1.2 (A) Signup and view all the answers

What role does the eyepiece play in a compound microscope?

It functions as a simple microscope or magnifier to enlarge the first image, producing the final virtual image. (C) Signup and view all the answers

What is the orientation of the final image produced by a compound microscope, relative to the original object?

Inverted. (A) Signup and view all the answers

If the magnification of the objective lens in a compound microscope is $m_O = 20$ and the magnification of the eyepiece is $m_e = 10$, what is the total magnification of the microscope?

200 (A) Signup and view all the answers

What does the 'tube length' (L) of a compound microscope represent?

The distance between the second focal point of the objective and the first focal point of the eyepiece. (D) Signup and view all the answers

In the equation $m_O = \frac{h'}{h} = \frac{L}{f_o}$ for the objective lens magnification, what does '$h'$ represent?

The height of the original object. (D) Signup and view all the answers

When the final image is formed at the near point of the eye, which formula is used to calculate the angular magnification ($m_e$) due to the eyepiece?

$m_e = 1 + (D/f_e)$ (B) Signup and view all the answers

In a compound microscope, if the objective lens has a focal length ($f_o$) of 5 mm, and the tube length (L) is 200 mm, what is the magnification ($m_O$) produced by the objective lens?

40 (B) Signup and view all the answers

Flashcards

Angle of Reflection

Angle between reflected ray and normal; equals the angle of incidence.

Angle of Incidence

Angle between incident ray and normal to the reflecting surface.