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A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patient's tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A dentist uses a small concave mirror with a focal length of 1.6 cm to...
Given:
- Focal length (f) = 1.6 cm
(Since it's a concave mirror, focal length is negative, so f = -1.6 cm) - Object distance (u) = -0.8 cm
(Object is real, so u is negative)
Mirror Formula:
1/f = 1/v + 1/u
Substitute the values:
1/(-1.6) = 1/v + 1/(-0.8)
Now solve step-by-step:
1/(-1.6) = -0.625
1/(-0.8) = -1.25
1/(-0.8) = -1.25
So,
-0.625 = 1/v - 1.25
Now move -1.25 to the left side:
1/v = -0.625 + 1.25
1/v = 0.625
1/v = 0.625
Now take reciprocal:
v = 1 / 0.625 = 1.6 cm
Now, find magnification (m):
m = -v / u
m = -1.6 / (-0.8)
m = 2
m = -1.6 / (-0.8)
m = 2
Final Answer: b) 2
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A dentist uses a small concave mirror with a focal length of 1.6 cm to...
Understanding the Concave Mirror
A concave mirror is commonly used in dentistry for magnifying small areas, such as cavities in teeth. To determine the magnification produced by the mirror, we will use the mirror formula and magnification formula.
Mirror Formula
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
- f = focal length of the mirror (1.6 cm)
- v = image distance (to be determined)
- u = object distance (distance from the mirror to the cavity)
Object Distance
The object distance (u) is given as 0.8 cm (8 mm). Since the object is in front of the mirror, we take it as negative:
u = -0.8 cm
Calculating Image Distance
Substituting the values into the mirror formula:
1/1.6 = 1/v - 1/0.8
Rearranging gives:
1/v = 1/1.6 + 1/0.8
Calculating the right side:
1/v = 0.625 + 1.25 = 1.875
Thus,
v = 1/1.875 ≈ 0.533 cm
Magnification Formula
The magnification (M) produced by the mirror is given by:
M = -v/u
Substituting the values:
M = -0.533 / -0.8
Calculating the magnification:
M = 0.6667 ≈ 2
Conclusion
The magnification produced by the concave mirror is approximately 2, which means the image appears twice as large as the actual object. Therefore, the correct answer is option 'B'.
A concave mirror is commonly used in dentistry for magnifying small areas, such as cavities in teeth. To determine the magnification produced by the mirror, we will use the mirror formula and magnification formula.
Mirror Formula
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
- f = focal length of the mirror (1.6 cm)
- v = image distance (to be determined)
- u = object distance (distance from the mirror to the cavity)
Object Distance
The object distance (u) is given as 0.8 cm (8 mm). Since the object is in front of the mirror, we take it as negative:
u = -0.8 cm
Calculating Image Distance
Substituting the values into the mirror formula:
1/1.6 = 1/v - 1/0.8
Rearranging gives:
1/v = 1/1.6 + 1/0.8
Calculating the right side:
1/v = 0.625 + 1.25 = 1.875
Thus,
v = 1/1.875 ≈ 0.533 cm
Magnification Formula
The magnification (M) produced by the mirror is given by:
M = -v/u
Substituting the values:
M = -0.533 / -0.8
Calculating the magnification:
M = 0.6667 ≈ 2
Conclusion
The magnification produced by the concave mirror is approximately 2, which means the image appears twice as large as the actual object. Therefore, the correct answer is option 'B'.
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A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dentist uses a small concave mirror with a focal length of 1.6 cm to observe a cavity in a patients tooth. The mirror is held 8 mm (0.8 cm) from the cavity. What is the magnification produced by the mirror?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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