Reflection and Refraction, Spherical Mirrors and Lenses
Reflection and Refraction, Spherical Mirrors and Lenses MCQ Questions
7.
What happens to the speed of light when it travels from air into water?
D.
Depends on the Wavelength
Approach
This question tests the understanding of how the speed of light changes when it passes from one medium to another. This phenomenon is governed by the refractive index of the media involved.
Step-by-step
- Understanding Refractive Index: The refractive index (\(n\)) of a medium is a measure of how much the speed of light is reduced when passing through that medium. It is defined as the ratio of the speed of light in a vacuum (\(c\)) to the speed of light in the medium (\(v\)):
\[ n = \frac{c}{v} \] - Comparing Refractive Indices: Air is considered an optically rarer medium, and its refractive index is approximately 1 (\(n_{\text{air}} \approx 1.0003\)). Water is an optically denser medium, and its refractive index is approximately 1.33 (\(n_{\text{water}} \approx 1.33\)).
- Relating Speed to Refractive Index: From the formula \(n = \frac{c}{v}\), we can derive the speed of light in a medium as \(v = \frac{c}{n}\).
- Applying to the Problem: Since the refractive index of water (\(n_{\text{water}} = 1.33\)) is greater than the refractive index of air (\(n_{\text{air}} = 1\)), the speed of light in water will be less than the speed of light in air.
\[ v_{\text{air}} = \frac{c}{n_{\text{air}}} = \frac{c}{1} = c \]
\[ v_{\text{water}} = \frac{c}{n_{\text{water}}} = \frac{c}{1.33} \]
Clearly, \(v_{\text{water}} < v_{\text{air}}\). - Conclusion: When light travels from air into water, its speed decreases.
Correct Option:
B) Decreases — As light enters a denser medium (water) from a rarer medium (air), its speed reduces because the refractive index of water is higher than that of air.
Incorrect Options
- A) Increases — The speed of light increases only when it travels from a denser medium to a rarer medium, which is the opposite of the given scenario.
- C) Remains the same — The speed of light remains the same only if it travels within the same medium or between two media with identical refractive indices, which is not the case here.
- D) Depends on the Wavelength — While the refractive index can slightly depend on the wavelength (dispersion), the fundamental change in speed from air to water is a decrease for all visible wavelengths. The primary factor determining the change in speed between two different media is their relative refractive indices, not the specific wavelength in this general context.
8.
The speed of light is maximum in
Approach
The speed of light depends on the medium through which it travels. This dependence is quantified by the refractive index of the medium. The higher the refractive index, the slower the speed of light in that medium.
Step-by-step
- Understand Refractive Index: The refractive index (\(n\)) of a medium is defined as the ratio of the speed of light in a vacuum (\(c\)) to the speed of light in that medium (\(v\)).
\[ n = \frac{c}{v} \] - Relate Speed of Light to Refractive Index: From the formula, we can express the speed of light in a medium as:
\[ v = \frac{c}{n} \]This equation shows that the speed of light (\(v\)) is inversely proportional to the refractive index (\(n\)). Therefore, for the speed of light to be maximum, the refractive index of the medium must be minimum. - Compare Refractive Indices: Let's consider the approximate refractive indices for the given options:
- Vacuum: \(n \approx 1.0000\) (Speed of light is maximum in vacuum)
- Air: \(n \approx 1.0003\)
- Water: \(n \approx 1.33\)
- Glass: \(n \approx 1.5 - 1.9\) (varies with type of glass)
- Diamond: \(n \approx 2.42\)
- Identify the Medium with Minimum Refractive Index: Among the given options, air has the lowest refractive index, which is very close to that of a vacuum.
- Conclusion: Since air has the lowest refractive index among the options, the speed of light will be maximum in air. While the absolute maximum speed of light is in a vacuum, among the given choices, air is the closest to a vacuum in terms of refractive index.
Correct Option:
A) Air — Air has the lowest refractive index among the given options (approximately 1.0003), meaning light travels fastest in it compared to water, glass, or diamond.
Incorrect Options
- B) Water — Water has a refractive index of approximately 1.33, which is higher than that of air. Therefore, light travels slower in water than in air.
- C) Glass — Glass has a refractive index typically ranging from 1.5 to 1.9, which is significantly higher than that of air. Light travels slower in glass than in air.
- D) Diamond — Diamond has a very high refractive index of approximately 2.42, making it the slowest medium for light among the given options.
9.
The critical angle for a medium-air boundary is 45 degrees. What is the refractive index of the medium?
Approach
The problem asks for the refractive index of a medium given its critical angle with respect to air. We can use the relationship between the critical angle and the refractive index, which is derived from Snell's Law for total internal reflection.
Step-by-step
Understand the Critical Angle: The critical angle (\(C\)) is the angle of incidence in a denser medium for which the angle of refraction in the rarer medium (air, in this case) is 90 degrees. Beyond this angle, total internal reflection occurs.
Recall Snell's Law: Snell's Law states that \(n_1 \sin \theta_1 = n_2 \sin \theta_2\), where \(n_1\) and \(n_2\) are the refractive indices of the first and second media, respectively, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction.
Apply Snell's Law to Critical Angle: For total internal reflection at the critical angle, light travels from the denser medium (refractive index \(n\)) to the rarer medium (air, refractive index \(n_{\text{air}} \approx 1\)). The angle of incidence is the critical angle \(C\), and the angle of refraction is \(90^\circ\).
So, we have:
\[ n \sin C = n_{\text{air}} \sin 90^\circ \]Substitute Known Values: We are given that the critical angle \(C = 45^\circ\). The refractive index of air \(n_{\text{air}} = 1\). We know that \(\sin 90^\circ = 1\).
Substituting these values into the equation:
\[ n \sin 45^\circ = 1 \times 1 \]\[ n \sin 45^\circ = 1 \]Calculate \(\sin 45^\circ\): The value of \(\sin 45^\circ\) is \(\frac{1}{\sqrt{2}}\).
So, the equation becomes:
\[ n \left( \frac{1}{\sqrt{2}} \right) = 1 \]Solve for \(n\):
\[ n = \sqrt{2} \]Calculate the numerical value: The approximate value of \(\sqrt{2}\) is 1.414.
Therefore, \(n \approx 1.41\).
Correct Option:
A) 1.41 is the calculated refractive index of the medium.
Incorrect Options
- B) 0.71: This value is approximately \(\frac{1}{\sqrt{2}}\) or \(\sin 45^\circ\). The refractive index must be greater than 1 for total internal reflection to occur from that medium into air. This would be the refractive index if the formula was incorrectly applied as \(n = \sin C\).
- C) 1: A refractive index of 1 corresponds to air or vacuum. If the medium had a refractive index of 1, there would be no critical angle for total internal reflection into air, as there would be no denser medium.
- D)
10.
Which type of mirror can form a real and inverted image?
ANSWER :
A. Concave mirror
Approach
This question tests knowledge about the image formation properties of different types of mirrors. Specifically, it asks which mirror can produce a real and inverted image. We need to recall the characteristics of images formed by concave, convex, and plane mirrors.
Step-by-step
- Understand Real and Inverted Images: A real image is formed when light rays actually converge at a point after reflection. Real images can be projected onto a screen. An inverted image means the image is upside down relative to the object.
- Analyze Concave Mirrors: Concave mirrors are converging mirrors. They can form both real and virtual images depending on the object's position. When an object is placed beyond the focal point of a concave mirror, the reflected rays converge to form a real, inverted, and magnified or diminished image. For example, if an object is placed between the center of curvature and the focal point, a real, inverted, and magnified image is formed beyond the center of curvature. If the object is beyond the center of curvature, a real, inverted, and diminished image is formed between the center of curvature and the focal point.
- Analyze Convex Mirrors: Convex mirrors are diverging mirrors. They always form virtual, erect, and diminished images, regardless of the object's position. The light rays appear to diverge from a point behind the mirror.
- Analyze Plane Mirrors: Plane mirrors always form virtual, erect, and same-sized images. The image is laterally inverted (left appears right and vice-versa).
- Conclusion: Based on the analysis, only a concave mirror can form a real and inverted image.
Correct Option: A) A concave mirror can form a real and inverted image when the object is placed beyond its focal point.
Incorrect Options
- B) Convex mirror — Convex mirrors always form virtual, erect, and diminished images. They never form real or inverted images.
- C) Plane mirror — Plane mirrors always form virtual, erect, and same-sized images. They never form real or inverted images.
- D) None of the above — This is incorrect because a concave mirror can form a real and inverted image.
11.
What is the angle of incidence when a light ray undergoes total internal reflection?
C.
Greater than the critical angle
ANSWER :
C. Greater than the critical angle
Approach
To determine the angle of incidence for total internal reflection, we need to recall the conditions under which this phenomenon occurs. Total internal reflection happens when light travels from a denser medium to a rarer medium and the angle of incidence exceeds a specific value known as the critical angle.
Step-by-step
-
Understand Total Internal Reflection (TIR): Total Internal Reflection is a phenomenon where the entire light incident on the interface between two media is reflected back into the denser medium. This occurs when two conditions are met:
- Light must travel from a denser medium to a rarer medium.
- The angle of incidence (\(i\)) in the denser medium must be greater than the critical angle (\(C\)) for that pair of media.
-
Define Critical Angle: The critical angle (\(C\)) is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90 degrees. At this angle, the refracted ray grazes the interface. According to Snell's Law:
\[ n_1 \sin(C) = n_2 \sin(90^\circ) \]
\[ n_1 \sin(C) = n_2 \]
\[ \sin(C) = \frac{n_2}{n_1} \]
where \(n_1\) is the refractive index of the denser medium and \(n_2\) is the refractive index of the rarer medium.
-
Condition for TIR: For total internal reflection to occur, the angle of incidence (\(i\)) must be strictly greater than the critical angle (\(C\)). If \(i = C\), the light ray refracts along the boundary. If \(i < C\), the light ray refracts into the rarer medium.
-
Conclusion: Therefore, when a light ray undergoes total internal reflection, its angle of incidence must be greater than the critical angle.
Correct Option: C) Greater than the critical angle
Incorrect Options
- A) 0 degrees — If the angle of incidence is 0 degrees, the light ray strikes the interface normally (perpendicularly) and passes straight through without deviation, regardless of the refractive indices. No reflection occurs in this case.
- B) 90 degrees — An angle of incidence of 90 degrees means the light ray is traveling parallel to the interface. In this scenario, the light ray would not enter the second medium at all, and thus total internal reflection cannot occur. The angle of incidence is measured with respect to the normal, so 90 degrees would mean the ray is parallel to the surface.
- D) None of the above — This is incorrect because option C accurately describes the condition for total internal reflection.
12.
What happens to the angle of reflection when a light ray strikes a surface at an angle of 45 degrees?
C.
It depends on the material of the surface
ANSWER :
A. It is 45 degrees
Approach
This question tests the fundamental laws of reflection in optics. The key principle to recall is the Law of Reflection, which states the relationship between the angle of incidence and the angle of reflection.
Step-by-step
- Understand the Law of Reflection: The first law of reflection states that the angle of incidence is equal to the angle of reflection. Both angles are measured with respect to the normal (an imaginary line perpendicular to the surface at the point of incidence).
- Identify the given information: The light ray strikes the surface at an angle of 45 degrees. In the context of reflection, when an angle is given without specifying if it's with respect to the normal or the surface, it is conventionally understood as the angle of incidence (the angle between the incident ray and the normal). If it were the angle with the surface, the question would typically specify "angle with the surface" or "grazing angle". Assuming it's the angle of incidence.
- Apply the Law of Reflection: According to the law, if the angle of incidence (\(\theta_i\)) is 45 degrees, then the angle of reflection (\(\theta_r\)) must also be 45 degrees.
\[ \theta_i = \theta_r \]\[ 45^{\circ} = \theta_r \]Correct Option:
A) It is 45 degrees. This is correct because, according to the Law of Reflection, the angle of incidence is always equal to the angle of reflection.
Incorrect Options
- B) It is 90 degrees. This is incorrect. An angle of reflection of 90 degrees would mean the reflected ray travels parallel to the surface, which only happens if the incident ray also strikes at 90 degrees to the normal (i.e., along the surface), which contradicts the given 45-degree angle of incidence.
- C) It depends on the material of the surface. This is incorrect. The Law of Reflection (angle of incidence equals angle of reflection) is a fundamental principle for all smooth, reflecting surfaces, regardless of the material. The material primarily affects the intensity of the reflected light, not the angle of reflection.
- D) None of the above. This is incorrect because option A correctly states the angle of reflection based on the Law of Reflection.
