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The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?
ans=30 but how?
ans=30 but how?
Most Upvoted Answer
The focal length of a convex lens is 20 cm At what distance from the l...
We know that m=v/u=h'/h given:h'=2h covex lens =)1/v - 1/u = 1/f let v be 2x and u be -x =)1/2x +1/x = -1/20 =)x + 2x/2x square = -1/20 =) 3x/2x square =-1/20 =)60 x =-2x square =)60/-2=x square/x =)-30=x(because object is always placed on left side) =)u=30
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The focal length of a convex lens is 20 cm At what distance from the l...
Introduction:
The focal length of a convex lens is 20 cm. We need to find the distance from the lens at which an object should be placed to obtain a two times larger and real image.
Given:
Focal length of convex lens (f) = 20 cm
Formula:
The formula relating the object distance (u), image distance (v), and focal length (f) of a lens is:
1/f = 1/v - 1/u
Where,
f = focal length of the lens
v = image distance
u = object distance
Step 1: Find the image distance for the given condition:
We are given that the image formed is two times larger than the object. This implies the magnification (m) is 2.
The formula for magnification is:
m = -v/u
Given m = 2, we can rearrange the formula to find the image distance (v):
v = -2u
Step 2: Substitute the values into the lens formula:
Now, we substitute the values of f and v into the lens formula:
1/20 = 1/(-2u) - 1/u
Step 3: Solve the equation:
To solve this equation, we can find a common denominator and simplify:
1/20 = -1/2u - 2/2u
1/20 = -3/2u
Cross-multiplying:
2u = -60
u = -30 cm
Step 4: Determine the positive distance:
The object distance (u) is calculated as -30 cm, but distance cannot be negative. Therefore, we take the positive value of u:
u = 30 cm
Conclusion:
So, the object should be placed at a distance of 30 cm from the lens in order to obtain a two times larger and real image.
The focal length of a convex lens is 20 cm. We need to find the distance from the lens at which an object should be placed to obtain a two times larger and real image.
Given:
Focal length of convex lens (f) = 20 cm
Formula:
The formula relating the object distance (u), image distance (v), and focal length (f) of a lens is:
1/f = 1/v - 1/u
Where,
f = focal length of the lens
v = image distance
u = object distance
Step 1: Find the image distance for the given condition:
We are given that the image formed is two times larger than the object. This implies the magnification (m) is 2.
The formula for magnification is:
m = -v/u
Given m = 2, we can rearrange the formula to find the image distance (v):
v = -2u
Step 2: Substitute the values into the lens formula:
Now, we substitute the values of f and v into the lens formula:
1/20 = 1/(-2u) - 1/u
Step 3: Solve the equation:
To solve this equation, we can find a common denominator and simplify:
1/20 = -1/2u - 2/2u
1/20 = -3/2u
Cross-multiplying:
2u = -60
u = -30 cm
Step 4: Determine the positive distance:
The object distance (u) is calculated as -30 cm, but distance cannot be negative. Therefore, we take the positive value of u:
u = 30 cm
Conclusion:
So, the object should be placed at a distance of 30 cm from the lens in order to obtain a two times larger and real image.
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The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how?
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The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how?.
The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The focal length of a convex lens is 20 cm At what distance from the lens should an object be placed so that a two times larger and real image may be obtained?ans=30 but how?.
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