Light: Mirrors and LensesClass 8 Science NCERT Solutions
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Q1End-of-Chapter Questions
A light ray is incident on a mirror and gets reflected by it (Fig. 10.21). The angle made by the incident ray with the normal to the mirror is . What is the angle made by the reflected ray with the mirror?
(i)
(ii)
(iii)
(iv)
Solution
Given:
The angle made by the incident ray with the normal to the mirror, which is the angle of incidence (i), is .
Angle of incidence, .
To Find:
The angle made by the reflected ray with the mirror.
Principle:
According to the first law of reflection, the angle of incidence is equal to the angle of reflection.
Where is the angle of reflection (the angle between the reflected ray and the normal).
Solution:
Using the law of reflection:
Angle of reflection, .
The normal is a line perpendicular to the mirror surface. Therefore, the angle between the normal and the mirror is .
The angle made by the reflected ray with the mirror is the difference between the angle of the normal to the mirror and the angle of reflection.
Angle with mirror =
Angle with mirror = .
Final Answer: The correct option is (ii) .
Q2End-of-Chapter Questions
Fig. 10.22 shows three different situations where a light ray falls on a mirror:
(i)
The light ray falls along the normal.
(ii)
The mirror is tilted, but the light ray still falls along the normal to the tilted surface.
(iii)
The mirror is tilted, and the light ray falls at an angle of from the normal. Draw the reflected ray in each case (Use a ruler and protractor for accurate drawing). What is the angle of reflection in each case?
Solution
Principle:
The law of reflection states that the angle of incidence () is equal to the angle of reflection (). The angle of incidence is the angle between the incident ray and the normal, and the angle of reflection is the angle between the reflected ray and the normal.
Solution:
(i) The light ray falls along the normal.
- Description of the reflected ray: When the incident ray falls along the normal, it strikes the mirror at a angle. The angle of incidence () is the angle between the incident ray and the normal, which in this case is .
- Angle of reflection: According to the law of reflection, . This means the reflected ray travels back along the same path as the incident ray.
(ii) The mirror is tilted, but the light ray still falls along the normal to the tilted surface.
- Description of the reflected ray: This situation is identical to case (i) with respect to the normal. The incident ray is along the normal of the tilted mirror. Therefore, the angle of incidence () is .
- Angle of reflection: The angle of reflection () will also be . The reflected ray will retrace its path along the normal.
(iii) The mirror is tilted, and the light ray falls at an angle of from the normal.
- Description of the reflected ray: The angle of incidence () is given as .
- Angle of reflection: According to the law of reflection, the angle of reflection () must be equal to the angle of incidence. Therefore, . The reflected ray will be on the opposite side of the normal from the incident ray, making an angle of with the normal.
Q3End-of-Chapter Questions
In Fig. 10.23, the cap of a sketch pen is placed in front of three types of mirrors. Match each image with the correct mirror.
Image Mirror (i) Plane mirror (ii) Convex mirror (iii) Concave mirror
Solution
Analysis of Images and Mirror Properties:
- Image (i): The image of the cap is erect (upright) and appears to be the same size as the object. This is the characteristic image formed by a plane mirror.
- Image (ii): The image of the cap is erect but smaller in size (diminished) than the object. This is the characteristic image formed by a convex mirror.
- Image (iii): The image of the cap is erect and larger in size (enlarged) than the object. This type of image is formed by a concave mirror when the object is placed close to it.
Matching:
- Image (i) matches with Plane mirror.
- Image (ii) matches with Convex mirror.
- Image (iii) matches with Concave mirror.
Final Answer:
| Image | Mirror |
|---|---|
| (i) | Plane mirror |
| (ii) | Convex mirror |
| (iii) | Concave mirror |
Q4End-of-Chapter Questions
In Fig. 10.24 the cap of a sketch pen is placed behind a convex lens, a concave lens, and a flat transparent glass piece - all at the same distance. Match each image with the correct type of lens or glass.
Image Lens/glass type (i) Flat transparent glass piece (ii) Convex lens (iii) Concave lens
Solution
Analysis of Images and Lens/Glass Properties:
- Image (i): The image of the cap is erect (upright) but smaller in size (diminished) than the object. This is the characteristic image seen through a concave lens.
- Image (ii): The image of the cap is erect and appears to be the same size as the object. Light passes through a flat transparent glass piece without significant magnification or minification.
- Image (iii): The image of the cap is erect and larger in size (enlarged) than the object. This type of image is seen through a convex lens when the object is placed close to it (as in a magnifying glass).
Matching:
- Image (i) matches with Concave lens.
- Image (ii) matches with Flat transparent glass piece.
- Image (iii) matches with Convex lens.
Final Answer:
| Image | Lens/glass type |
|---|---|
| (i) | Concave lens |
| (ii) | Flat transparent glass piece |
| (iii) | Convex lens |
Q5End-of-Chapter Questions
When the light is incident along the normal on the mirror, which of the following statements is true:
(i)
Angle of incidence is
(ii)
Angle of incidence is
(iii)
Angle of reflection is
(iv)
No reflection of light takes place in this case
Solution
Definition:
The angle of incidence is defined as the angle between the incident ray and the normal to the reflecting surface at the point of incidence.
Analysis:
When a light ray is incident along the normal, the incident ray itself lies on the normal line. Therefore, the angle between the incident ray and the normal is zero.
Angle of incidence, .
According to the law of reflection, the angle of reflection () is equal to the angle of incidence (). So, . The light reflects back along the same path.
Conclusion:
Statement (ii) is the correct description of this situation.
Final Answer: The correct option is (ii) Angle of incidence is .
Q6End-of-Chapter Questions
Three mirrors-plane, concave and convex are placed in Fig. 10.25. On the basis of the images of the graph sheet formed in the mirrors, identify the mirrors and write their names above the mirrors.
Solution
Analysis of Images and Mirror Properties:
To identify the mirrors, we observe how the grid lines of the graph sheet appear in each reflection.
-
Mirror on the left: The image of the graph sheet shows squares that are the same size as the original grid. The image is not distorted in size. This is the characteristic of a plane mirror.
-
Mirror in the middle: The image of the graph sheet shows squares that are larger than the original grid. The grid lines are magnified. This enlarging effect is produced by a concave mirror when the object is close.
-
Mirror on the right: The image of the graph sheet shows squares that are smaller than the original grid. The grid lines are diminished, and a wider area of the grid is visible. This is the characteristic of a convex mirror.
Final Answer:
From left to right, the mirrors are:
- Plane mirror
- Concave mirror
- Convex mirror
Q7End-of-Chapter Questions
In a museum, a woman walks towards a large convex mirror (Fig. 10.26). She will see that:
(i)
her erect image keeps decreasing in size.
(ii)
her inverted image keeps decreasing in size.
(iii)
her inverted image keeps increasing in size and eventually it becomes erect and magnified.
(iv)
her erect image keeps increasing in size.
Solution
Properties of a Convex Mirror:
A convex mirror always forms a virtual, erect, and diminished (smaller than the object) image, regardless of the object's distance from the mirror.
Analysis of the Situation:
- Image Orientation: The image formed by a convex mirror is always erect. This eliminates options (ii) and (iii).
- Image Size Change: As an object moves closer to a convex mirror, its image also moves closer to the mirror and increases in size. However, the image size will always be smaller than the object's actual size.
Conclusion:
As the woman walks towards the convex mirror, her erect image will keep increasing in size.
Final Answer: The correct option is (iv) her erect image keeps increasing in size.
Q8End-of-Chapter Questions
Hold a magnifying glass over text and identify the distance where you can see the text bigger than they are written. Now move it away from the text. What do you notice? Which type of lens is a magnifying glass?
Solution
Type of Lens:
A magnifying glass is a convex lens.
Observations:
-
Close Distance: When a magnifying glass (convex lens) is held close to the text, the letters appear erect (upright) and magnified (bigger than their actual size). This is because a convex lens forms a virtual, erect, and enlarged image when the object is placed within its focal length.
-
Moving it Away: As you slowly move the magnifying glass away from the text, the magnified image remains erect for a certain distance. Beyond a specific point (the focal point), the image flips and becomes inverted (upside down). The size of this inverted image changes as you move the lens further away; it can be enlarged, the same size, or diminished depending on the distance.
Final Answer:
A magnifying glass is a convex lens. When held close to text, it shows an enlarged and erect image. As it is moved away from the text, the image becomes inverted.
Q9End-of-Chapter Questions
Match the entries in Column I with those in Column II.
Column I Column II (i) Concave mirror (a) Spherical mirror with a reflecting surface that curves inwards. (ii) Convex mirror (b) It forms an image which is always erect and diminished in size. (iii) Convex lens (c) Object placed behind it may appear inverted at some distance. (iv) Concave lens (d) Object placed behind it always appears diminished in size.
Solution
Analysis and Matching:
-
(i) Concave mirror: By definition, a concave mirror has a reflecting surface that is curved inwards. So, (i) matches with (a).
-
(ii) Convex mirror: A convex mirror always forms an image that is virtual, erect, and diminished in size, regardless of the object's position. So, (ii) matches with (b).
-
(iii) Convex lens: A convex lens can form an enlarged, erect image when the object is close. However, as the object is moved farther away (beyond the focal point), the image becomes real and inverted. So, (iii) matches with (c).
-
(iv) Concave lens: A concave lens always forms an image that is virtual, erect, and diminished in size. So, (iv) matches with (d).
Final Answer:
(i)
Concave mirror → (a) Spherical mirror with a reflecting surface that curves inwards.
*
(ii)
Convex mirror → (b) It forms an image which is always erect and diminished in size.
*
(iii)
Convex lens → (c) Object placed behind it may appear inverted at some distance.
*
(iv)
Concave lens → (d) Object placed behind it always appears diminished in size.
Q10End-of-Chapter Questions
The following question is based on Assertion/Reason. Assertion: Convex mirrors are preferred for observing the traffic behind us. Reason: Convex mirrors provide a significantly larger view area than plane mirrors. Choose the correct option:
(i)
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(ii)
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
(iii)
Assertion is correct but Reason is incorrect.
(iv)
Both Assertion and Reason are incorrect.
Solution
Analysis of Assertion:
The assertion states that convex mirrors are preferred for observing traffic behind us (e.g., as side-view mirrors on vehicles). This is a correct statement.
Analysis of Reason:
The reason states that convex mirrors provide a significantly larger view area than plane mirrors of the same size. This is also correct. Because a convex mirror's surface is curved outwards, it reflects light from a wider angle, giving the driver a larger field of view of the road behind.
Relationship between Assertion and Reason:
The reason (larger view area) is the primary advantage and the correct explanation for why convex mirrors are used as rear-view mirrors (Assertion). They allow drivers to see more of the traffic and potential hazards behind them.
Conclusion:
Both the Assertion and the Reason are correct, and the Reason is the correct explanation for the Assertion.
Final Answer: The correct option is (i) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
Q11End-of-Chapter Questions
In Fig. 10.27, note that O stands for object, M for mirror, and I for image. Which of the following statements is true?
(i)
Figure (a) indicates a plane mirror and Figure (b) indicates a concave mirror.
(ii)
Figure (a) indicates a convex mirror and Figure (b) indicates a concave mirror.
(iii)
Figure (a) indicates a concave mirror and Figure (b) indicates a convex mirror.
(iv)
Figure (a) indicates a plane mirror and Figure (b) indicates a convex mirror.
Solution
Analysis of Figure (a):
The diagram shows an object (O) placed in front of a mirror (M). The image (I) formed is erect (upright) and diminished (smaller than the object). An erect and diminished image is always formed by a convex mirror.
Analysis of Figure (b):
The diagram shows an object (O) placed in front of a mirror (M). The image (I) formed is erect (upright) and enlarged (larger than the object). An erect and enlarged image is formed by a concave mirror when the object is placed very close to it (within its focal length).
Conclusion:
- Figure (a) shows a convex mirror.
- Figure (b) shows a concave mirror.
This matches the statement in option (ii).
Final Answer: The correct option is (ii) Figure (a) indicates a convex mirror and Figure (b) indicates a concave mirror.
Q12End-of-Chapter Questions
Place a pencil behind a transparent glass tumbler (Fig. 10.28a). Now fill the tumbler halfway with water (Fig. 10.28b). How does the pencil appear when viewed through the water? Explain why its shape appears changed.
Solution
Observation:
When viewed through the water in the tumbler, the part of the pencil submerged in water appears to be bent at the surface of the water. It also appears thicker or magnified when viewed from the side.
Explanation:
This phenomenon is caused by the refraction of light. Refraction is the bending of light as it passes from one medium to another (in this case, from water to air).
-
Apparent Bending: Light rays traveling from the submerged part of the pencil pass from water (a denser medium) into air (a rarer medium) before reaching the observer's eyes. When light enters a rarer medium from a denser medium, it bends away from the normal (an imaginary line perpendicular to the surface).
-
Our eyes perceive objects based on the assumption that light travels in straight lines. Therefore, our brain traces these bent rays back in a straight line to a point that is shallower than the pencil's actual position. This makes the submerged part of the pencil appear raised and bent at the water's surface.
-
Apparent Thickness/Magnification: The curved surface of the glass tumbler filled with water acts like a convex lens. When the pencil is viewed from the side, this lens effect magnifies the image of the pencil, making it appear thicker than it actually is.
Final Answer: The pencil appears bent at the water's surface and may also look thicker. This change in appearance is due to the refraction of light as it passes from water to air, and the magnifying effect of the curved, water-filled glass.