光学機器、光路差および屈折
導入済み| English | 意味 |
|---|---|
| resolving power/rɪˈzɒlvɪŋ ˈpaʊə/ | 分解能 |
| optical path length/ˈɒptɪkl pæθ leŋθ/ | 光路長 |
A decision before an answer
- A gas cell in one arm of a Michelson interferometer is crossed twice. Counting only one passage halves the inferred refractive-index change.
- Your goal: Calculate telescope magnification and grating resolving power.
Read the relationship
- For an ideal astronomical telescope adjusted for relaxed viewing at infinity, the objective forms its focal-plane image and the eyepiece collimates the emerging light. Lens separation is f_objective+f_eyepiece; angular magnification magnitude is f_objective/f_eyepiece. The usual two-converging-lens telescope produces an inverted image, represented by a negative signed angular magnification under a consistent convention. A finite final-image distance changes lens separation; do not use the infinity adjustment without checking the condition.
- Relate Michelson fringe counts to double-pass optical path changes.
A relaxed-view telescope has separation 72 cm and eyepiece focal length 12 cm. Angular magnification magnitude is:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
Objective focal length is 72−12=60 cm; 60/12=5.
Use the defining rule
- Resolving power R=λ/Δλ describes the smallest distinguishable wavelength separation near λ. For an ideal diffraction grating in order m with N illuminated slits, R=mN. This is a resolution criterion, not simply the angular position formula d sinθ=mλ. Increasing illuminated slit count sharpens the principal peaks; increasing slit spacing mainly changes their angular locations. A measured λ=600 nm and Δλ=3 nm gives R=200, independent of converting both lengths to metres because their ratio uses matching units.
- Trace surface normals before applying Snell and reflection laws.
A grating just resolves 400 nm and 402 nm. Approximate resolving power is:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
R≈400/2=200; wavelength and separation use the same units.
Check the conditions
- Michelson interference depends on the optical path difference between the arms. If one arm contains a gas cell of geometric length L and index changes from n to 1 upon evacuation, a double passage changes path by 2L(n−1). If N fringes pass, the magnitude of this change is Nλ, so n−1=Nλ/(2L). For a moving mirror instead, displacement Δx gives path change 2Δx. Fringes count phase cycles; one fringe is one wavelength of optical path, not one wavelength of mirror motion.
- Trace surface normals before applying Snell and reflection laws.
A relaxed-view telescope has lens separation 80 cm and eyepiece focal length 16 cm. Its objective focal length is 64 cm and magnification magnitude is 4. Evacuating a 5 cm gas cell causes 80 fringes at wavelength 500 nm: n−1=80·500×10⁻⁹/(2·0.05)=0.0004. The initial gas index is 1.0004, not 1.0008.
Moving one Michelson mirror by 150 nm changes round-trip optical path by ____ nm.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
The light crosses the changed distance outbound and returning.
Apply the task format
- Snell’s law n1 sinθ1=n2 sinθ2 uses angles from the local surface normal. Reflection has equal incoming and outgoing angles from that same normal. In a rectangular block, normals of neighbouring faces are perpendicular: an incidence angle measured from one normal is complementary to the angle of that same ray from the other. Draw the ray and normals before substitution. For incidence from index n into air, total internal reflection occurs only when sinθ>1/n; equality is the critical grazing case. A stated partly refracted ray must satisfy the transmission condition.
- Trace surface normals before applying Snell and reflection laws.
Use optical path, not just geometric distance. Refraction angles are measured from the normal of the actual surface, and telescope focal-length addition assumes a final image at infinity.
このケースに当てはまる答えはどれか？
望遠鏡の倍率と回折格子の分解能を計算する
Snell’s-law angles should be measured from the surface itself.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
They are measured from its normal; the surface angle is complementary.
Keep the distinctions
- resolving power 分辨本领 — Wavelength divided by the smallest resolvable wavelength separation.
- optical path length 光程 — Geometric path weighted by refractive index along the ray.
- Calculate telescope magnification and grating resolving power.
- Relate Michelson fringe counts to double-pass optical path changes.
- Trace surface normals before applying Snell and reflection laws.
Match each term with its precise meaning in this lesson.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
The order follows the stated process; check each stage before the next.