364731
Assertion : A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length. Reason : The refractive index of water is smaller than the refractive index of air.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
A concave mirror and a convex lens both have the same focal length in air. This is incorrect. Concave mirrors and convex lenses do not inherently have the same focal length in air. Their focal lengths depend on the radii of curvature of their surfaces and the refractive indices of the surrounding media. The refractive index of water is smaller than the refractive index of air. This is not correct. In reality, the refractive index of water (typically around 1.33) is greater than the refractive index of air (which is approximately 1). Therefore, the Reason's explanation is incorrect. The correct explanation is that the focal length of a mirror doesn't depend on the refractive index of the surrounding medium, while the focal length of a lens does depend on the refractive index of the surrounding medium. As a result, when a lens is submerged in a medium with a higher refractive index (like water), its focal length increases. The Assertion is correct in stating that the concave mirror and convex lens may have the same focal length in air, but the Reason's explanation is not accurate.
AIIMS - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364732
Image formed by a concave mirror of focal length \(6\;cm\), is 3 times of the object, then the distance of object from mirror is
364733
An object is placed at a distance of \(20\;cm\) from the pole of a concave mirror of focal length \(10\;cm\). The distance of the image formed is
1 \( + 20\;cm\)
2 \( + 10\;cm\)
3 \( - 20\;cm\)
4 \( - 10\;cm\)
Explanation:
Here, as per the Cartesian sign convention, object distance, \(u = - 20cm\) Focal length of the mirror, \(f = - 10cm\)
364734
A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of \(30\;cm\)?
1 \(30\;cm\)
2 \(20\;cm\)
3 \(10\;cm\)
4 \(90\;cm\)
Explanation:
As radius of curvature(R) is negative for a concave mirror, \(R = - 30\;{\rm{cm}}.\) \(\therefore \) The focal length of the mirror is \(f = \frac{R}{2} = \frac{{ - 30cm}}{2} = - 15cm\) As the person wants his real enlarged image,
magnification \(m = - \frac{v}{u} = - 3 \Rightarrow v = 3u\) According to mirror formula, \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) \(\therefore \,\,\,\,\,\frac{1}{{3u}} + \frac{1}{u} = \frac{1}{{ - 15cm}}\) \( \Rightarrow u = \frac{{ - 60cm}}{3} = - 20\,{\rm{cm}}\) -ve sign shows that the person should stand in front of the mirror.
KCET - 2015
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364735
The sun (diameter \(D\)) subtends an angle of 2 rad at the pole of a concave mirror of focal length \(f\). The diameter of the image of the sun formed by the mirror is
1 \(D\,\theta \)
2 \(2f\,\theta \)
3 \(1\,f\,\theta \)
4 \(f\,\theta \)
Explanation:
Since, the sun is at very large distance, \(u = \infty \) The image will be formed at the focus \(\tan \theta = \frac{{d/2}}{f} = \theta \) \(d = 2f\theta \)
364731
Assertion : A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length. Reason : The refractive index of water is smaller than the refractive index of air.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
A concave mirror and a convex lens both have the same focal length in air. This is incorrect. Concave mirrors and convex lenses do not inherently have the same focal length in air. Their focal lengths depend on the radii of curvature of their surfaces and the refractive indices of the surrounding media. The refractive index of water is smaller than the refractive index of air. This is not correct. In reality, the refractive index of water (typically around 1.33) is greater than the refractive index of air (which is approximately 1). Therefore, the Reason's explanation is incorrect. The correct explanation is that the focal length of a mirror doesn't depend on the refractive index of the surrounding medium, while the focal length of a lens does depend on the refractive index of the surrounding medium. As a result, when a lens is submerged in a medium with a higher refractive index (like water), its focal length increases. The Assertion is correct in stating that the concave mirror and convex lens may have the same focal length in air, but the Reason's explanation is not accurate.
AIIMS - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364732
Image formed by a concave mirror of focal length \(6\;cm\), is 3 times of the object, then the distance of object from mirror is
364733
An object is placed at a distance of \(20\;cm\) from the pole of a concave mirror of focal length \(10\;cm\). The distance of the image formed is
1 \( + 20\;cm\)
2 \( + 10\;cm\)
3 \( - 20\;cm\)
4 \( - 10\;cm\)
Explanation:
Here, as per the Cartesian sign convention, object distance, \(u = - 20cm\) Focal length of the mirror, \(f = - 10cm\)
364734
A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of \(30\;cm\)?
1 \(30\;cm\)
2 \(20\;cm\)
3 \(10\;cm\)
4 \(90\;cm\)
Explanation:
As radius of curvature(R) is negative for a concave mirror, \(R = - 30\;{\rm{cm}}.\) \(\therefore \) The focal length of the mirror is \(f = \frac{R}{2} = \frac{{ - 30cm}}{2} = - 15cm\) As the person wants his real enlarged image,
magnification \(m = - \frac{v}{u} = - 3 \Rightarrow v = 3u\) According to mirror formula, \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) \(\therefore \,\,\,\,\,\frac{1}{{3u}} + \frac{1}{u} = \frac{1}{{ - 15cm}}\) \( \Rightarrow u = \frac{{ - 60cm}}{3} = - 20\,{\rm{cm}}\) -ve sign shows that the person should stand in front of the mirror.
KCET - 2015
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364735
The sun (diameter \(D\)) subtends an angle of 2 rad at the pole of a concave mirror of focal length \(f\). The diameter of the image of the sun formed by the mirror is
1 \(D\,\theta \)
2 \(2f\,\theta \)
3 \(1\,f\,\theta \)
4 \(f\,\theta \)
Explanation:
Since, the sun is at very large distance, \(u = \infty \) The image will be formed at the focus \(\tan \theta = \frac{{d/2}}{f} = \theta \) \(d = 2f\theta \)
364731
Assertion : A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length. Reason : The refractive index of water is smaller than the refractive index of air.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
A concave mirror and a convex lens both have the same focal length in air. This is incorrect. Concave mirrors and convex lenses do not inherently have the same focal length in air. Their focal lengths depend on the radii of curvature of their surfaces and the refractive indices of the surrounding media. The refractive index of water is smaller than the refractive index of air. This is not correct. In reality, the refractive index of water (typically around 1.33) is greater than the refractive index of air (which is approximately 1). Therefore, the Reason's explanation is incorrect. The correct explanation is that the focal length of a mirror doesn't depend on the refractive index of the surrounding medium, while the focal length of a lens does depend on the refractive index of the surrounding medium. As a result, when a lens is submerged in a medium with a higher refractive index (like water), its focal length increases. The Assertion is correct in stating that the concave mirror and convex lens may have the same focal length in air, but the Reason's explanation is not accurate.
AIIMS - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364732
Image formed by a concave mirror of focal length \(6\;cm\), is 3 times of the object, then the distance of object from mirror is
364733
An object is placed at a distance of \(20\;cm\) from the pole of a concave mirror of focal length \(10\;cm\). The distance of the image formed is
1 \( + 20\;cm\)
2 \( + 10\;cm\)
3 \( - 20\;cm\)
4 \( - 10\;cm\)
Explanation:
Here, as per the Cartesian sign convention, object distance, \(u = - 20cm\) Focal length of the mirror, \(f = - 10cm\)
364734
A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of \(30\;cm\)?
1 \(30\;cm\)
2 \(20\;cm\)
3 \(10\;cm\)
4 \(90\;cm\)
Explanation:
As radius of curvature(R) is negative for a concave mirror, \(R = - 30\;{\rm{cm}}.\) \(\therefore \) The focal length of the mirror is \(f = \frac{R}{2} = \frac{{ - 30cm}}{2} = - 15cm\) As the person wants his real enlarged image,
magnification \(m = - \frac{v}{u} = - 3 \Rightarrow v = 3u\) According to mirror formula, \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) \(\therefore \,\,\,\,\,\frac{1}{{3u}} + \frac{1}{u} = \frac{1}{{ - 15cm}}\) \( \Rightarrow u = \frac{{ - 60cm}}{3} = - 20\,{\rm{cm}}\) -ve sign shows that the person should stand in front of the mirror.
KCET - 2015
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364735
The sun (diameter \(D\)) subtends an angle of 2 rad at the pole of a concave mirror of focal length \(f\). The diameter of the image of the sun formed by the mirror is
1 \(D\,\theta \)
2 \(2f\,\theta \)
3 \(1\,f\,\theta \)
4 \(f\,\theta \)
Explanation:
Since, the sun is at very large distance, \(u = \infty \) The image will be formed at the focus \(\tan \theta = \frac{{d/2}}{f} = \theta \) \(d = 2f\theta \)
364731
Assertion : A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length. Reason : The refractive index of water is smaller than the refractive index of air.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
A concave mirror and a convex lens both have the same focal length in air. This is incorrect. Concave mirrors and convex lenses do not inherently have the same focal length in air. Their focal lengths depend on the radii of curvature of their surfaces and the refractive indices of the surrounding media. The refractive index of water is smaller than the refractive index of air. This is not correct. In reality, the refractive index of water (typically around 1.33) is greater than the refractive index of air (which is approximately 1). Therefore, the Reason's explanation is incorrect. The correct explanation is that the focal length of a mirror doesn't depend on the refractive index of the surrounding medium, while the focal length of a lens does depend on the refractive index of the surrounding medium. As a result, when a lens is submerged in a medium with a higher refractive index (like water), its focal length increases. The Assertion is correct in stating that the concave mirror and convex lens may have the same focal length in air, but the Reason's explanation is not accurate.
AIIMS - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364732
Image formed by a concave mirror of focal length \(6\;cm\), is 3 times of the object, then the distance of object from mirror is
364733
An object is placed at a distance of \(20\;cm\) from the pole of a concave mirror of focal length \(10\;cm\). The distance of the image formed is
1 \( + 20\;cm\)
2 \( + 10\;cm\)
3 \( - 20\;cm\)
4 \( - 10\;cm\)
Explanation:
Here, as per the Cartesian sign convention, object distance, \(u = - 20cm\) Focal length of the mirror, \(f = - 10cm\)
364734
A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of \(30\;cm\)?
1 \(30\;cm\)
2 \(20\;cm\)
3 \(10\;cm\)
4 \(90\;cm\)
Explanation:
As radius of curvature(R) is negative for a concave mirror, \(R = - 30\;{\rm{cm}}.\) \(\therefore \) The focal length of the mirror is \(f = \frac{R}{2} = \frac{{ - 30cm}}{2} = - 15cm\) As the person wants his real enlarged image,
magnification \(m = - \frac{v}{u} = - 3 \Rightarrow v = 3u\) According to mirror formula, \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) \(\therefore \,\,\,\,\,\frac{1}{{3u}} + \frac{1}{u} = \frac{1}{{ - 15cm}}\) \( \Rightarrow u = \frac{{ - 60cm}}{3} = - 20\,{\rm{cm}}\) -ve sign shows that the person should stand in front of the mirror.
KCET - 2015
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364735
The sun (diameter \(D\)) subtends an angle of 2 rad at the pole of a concave mirror of focal length \(f\). The diameter of the image of the sun formed by the mirror is
1 \(D\,\theta \)
2 \(2f\,\theta \)
3 \(1\,f\,\theta \)
4 \(f\,\theta \)
Explanation:
Since, the sun is at very large distance, \(u = \infty \) The image will be formed at the focus \(\tan \theta = \frac{{d/2}}{f} = \theta \) \(d = 2f\theta \)
364731
Assertion : A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length. Reason : The refractive index of water is smaller than the refractive index of air.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Both Assertion and Reason are incorrect.
Explanation:
A concave mirror and a convex lens both have the same focal length in air. This is incorrect. Concave mirrors and convex lenses do not inherently have the same focal length in air. Their focal lengths depend on the radii of curvature of their surfaces and the refractive indices of the surrounding media. The refractive index of water is smaller than the refractive index of air. This is not correct. In reality, the refractive index of water (typically around 1.33) is greater than the refractive index of air (which is approximately 1). Therefore, the Reason's explanation is incorrect. The correct explanation is that the focal length of a mirror doesn't depend on the refractive index of the surrounding medium, while the focal length of a lens does depend on the refractive index of the surrounding medium. As a result, when a lens is submerged in a medium with a higher refractive index (like water), its focal length increases. The Assertion is correct in stating that the concave mirror and convex lens may have the same focal length in air, but the Reason's explanation is not accurate.
AIIMS - 2008
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364732
Image formed by a concave mirror of focal length \(6\;cm\), is 3 times of the object, then the distance of object from mirror is
364733
An object is placed at a distance of \(20\;cm\) from the pole of a concave mirror of focal length \(10\;cm\). The distance of the image formed is
1 \( + 20\;cm\)
2 \( + 10\;cm\)
3 \( - 20\;cm\)
4 \( - 10\;cm\)
Explanation:
Here, as per the Cartesian sign convention, object distance, \(u = - 20cm\) Focal length of the mirror, \(f = - 10cm\)
364734
A person wants a real image of his own, 3 times enlarged. Where should he stand in front of a concave mirror of radius of curvature of \(30\;cm\)?
1 \(30\;cm\)
2 \(20\;cm\)
3 \(10\;cm\)
4 \(90\;cm\)
Explanation:
As radius of curvature(R) is negative for a concave mirror, \(R = - 30\;{\rm{cm}}.\) \(\therefore \) The focal length of the mirror is \(f = \frac{R}{2} = \frac{{ - 30cm}}{2} = - 15cm\) As the person wants his real enlarged image,
magnification \(m = - \frac{v}{u} = - 3 \Rightarrow v = 3u\) According to mirror formula, \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) \(\therefore \,\,\,\,\,\frac{1}{{3u}} + \frac{1}{u} = \frac{1}{{ - 15cm}}\) \( \Rightarrow u = \frac{{ - 60cm}}{3} = - 20\,{\rm{cm}}\) -ve sign shows that the person should stand in front of the mirror.
KCET - 2015
PHXII09:RAY OPTICS AND OPTICAL INSTRUMENTS
364735
The sun (diameter \(D\)) subtends an angle of 2 rad at the pole of a concave mirror of focal length \(f\). The diameter of the image of the sun formed by the mirror is
1 \(D\,\theta \)
2 \(2f\,\theta \)
3 \(1\,f\,\theta \)
4 \(f\,\theta \)
Explanation:
Since, the sun is at very large distance, \(u = \infty \) The image will be formed at the focus \(\tan \theta = \frac{{d/2}}{f} = \theta \) \(d = 2f\theta \)
