Class 10 Exam > Class 10 Questions > You are provided with a convex lens of F = 50...
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You are provided with a convex lens of F = 50 cm. To obtain a smaller inverted image, the distance of the object from the lens should be
- a)50 cm
- b)75 cm
- c)100 cm
- d)120 cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
You are provided with a convex lens of F = 50 cm. To obtain a smaller ...
Explanation:
To obtain a smaller inverted image using a convex lens, we need to place the object at a certain distance from the lens. The distance of the object from the lens can be determined using the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- u is the distance of the object from the lens
- v is the distance of the image from the lens
In this case, the focal length of the lens is given as 50 cm.
Step 1: Identify the given information
- Focal length (f) = 50 cm
Step 2: Determine the required conditions for a smaller inverted image
To obtain a smaller inverted image, the image distance (v) should be smaller than the object distance (u). This can be achieved by placing the object beyond the focal point of the lens.
Step 3: Apply the lens formula to find the object distance
Substituting the given values into the lens formula:
1/50 = 1/v - 1/u
Simplifying the equation:
1/v = 1/50 + 1/u
To obtain a smaller inverted image, the value of 1/v should be smaller than 1/50. This implies that the value of 1/u should be greater than 1/50.
Step 4: Determine the object distance
To find the object distance that satisfies the condition, we can substitute different values of u and solve the equation.
Let's try option D: 1/120 = 1/50 + 1/u
Simplifying the equation:
1/u = 1/120 - 1/50
1/u = (5 - 12)/(120 * 50)
1/u = -7/6000
The value of 1/u is negative, indicating that the object is placed on the same side as the lens. This is the correct condition to obtain a smaller inverted image.
Therefore, the correct answer is option D: 120 cm, as it satisfies the conditions for obtaining a smaller inverted image.
To obtain a smaller inverted image using a convex lens, we need to place the object at a certain distance from the lens. The distance of the object from the lens can be determined using the lens formula:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens
- u is the distance of the object from the lens
- v is the distance of the image from the lens
In this case, the focal length of the lens is given as 50 cm.
Step 1: Identify the given information
- Focal length (f) = 50 cm
Step 2: Determine the required conditions for a smaller inverted image
To obtain a smaller inverted image, the image distance (v) should be smaller than the object distance (u). This can be achieved by placing the object beyond the focal point of the lens.
Step 3: Apply the lens formula to find the object distance
Substituting the given values into the lens formula:
1/50 = 1/v - 1/u
Simplifying the equation:
1/v = 1/50 + 1/u
To obtain a smaller inverted image, the value of 1/v should be smaller than 1/50. This implies that the value of 1/u should be greater than 1/50.
Step 4: Determine the object distance
To find the object distance that satisfies the condition, we can substitute different values of u and solve the equation.
Let's try option D: 1/120 = 1/50 + 1/u
Simplifying the equation:
1/u = 1/120 - 1/50
1/u = (5 - 12)/(120 * 50)
1/u = -7/6000
The value of 1/u is negative, indicating that the object is placed on the same side as the lens. This is the correct condition to obtain a smaller inverted image.
Therefore, the correct answer is option D: 120 cm, as it satisfies the conditions for obtaining a smaller inverted image.
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Community Answer
You are provided with a convex lens of F = 50 cm. To obtain a smaller ...
Step 1: Determine if the focal length is positive or negative.
Step 2: Determine if the image distance is positive or negative.
Step 3: Use the equation
Step 2: Determine if the image distance is positive or negative.
Step 3: Use the equation
to calculate the distance of the object from the lens.
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You are provided with a convex lens of F = 50 cm. To obtain a smaller inverted image, the distance of the object from the lens should bea)50 cmb)75 cmc)100 cmd)120 cmCorrect answer is option 'D'. Can you explain this answer?
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